(a) Data Gathering and Integration
library(dplyr)##
## Attaching package: 'dplyr'## The following objects are masked from 'package:stats':
##
## filter, lag## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, unionStats <- read.csv("C:/Users/charan/OneDrive/Desktop/dump/Seasons_Stats.csv", header=FALSE)
salary_1718 <- read.csv("C:/Users/charan/OneDrive/Desktop/reg-project/NBA_season1718_salary.csv", header=FALSE)# rm(per_game_stats)Here I am using two datasets, one is the stats dataset and other is the Salary dataset.
Stats:
This dataset contains detailed performance metrics for NBA players from the year 1950 to 2017. It includes various statistics, such as points, assists, rebounds, and more, which are crucial for building features.
Salary_1718:
This includes the salaries of NBA players for the 2017-2018 season. This serves as the target variable for the regression model, providing the actual salaries that we aim to predict.
Filtering and Merging
Since we are trying to predict the salaries of the players for the 17-18 Season on basis of their performance in 16-17 season, We do not require all data present in Stats dataset,hence we will filter it out in accordance to our objective.
First Let’s rename the columns:
colnames(Stats) <- c("Sl.no","Year", "Player", "Pos", "Age", "Tm", "G", "GS", "MP", "PER", "TS%", "3PAr", "FTr", "ORB%", "DRB%", "TRB%", "AST%", "STL%", "BLK%", "TOV%", "USG%", "blank1", "OWS", "DWS", "WS", "WS/48", "blank2", "OBPM", "DBPM", "BPM", "VORP", "FG", "FGA", "FG%", "3P", "3PA", "3P%", "2P", "2PA", "2P%", "eFG%", "FT", "FTA", "FT%", "ORB", "DRB", "TRB", "AST", "STL", "BLK", "TOV", "PF", "PTS")
Stats <- Stats[-1, ]
head(Stats)## Sl.no Year Player Pos Age Tm G GS MP PER TS% 3PAr FTr ORB%
## 2 0 1950 Curly Armstrong G-F 31 FTW 63 0.368 0.467
## 3 1 1950 Cliff Barker SG 29 INO 49 0.435 0.387
## 4 2 1950 Leo Barnhorst SF 25 CHS 67 0.394 0.259
## 5 3 1950 Ed Bartels F 24 TOT 15 0.312 0.395
## 6 4 1950 Ed Bartels F 24 DNN 13 0.308 0.378
## 7 5 1950 Ed Bartels F 24 NYK 2 0.376 0.75
## DRB% TRB% AST% STL% BLK% TOV% USG% blank1 OWS DWS WS WS/48 blank2 OBPM
## 2 -0.1 3.6 3.5
## 3 1.6 0.6 2.2
## 4 0.9 2.8 3.6
## 5 -0.5 -0.1 -0.6
## 6 -0.5 -0.1 -0.6
## 7 0 0 0
## DBPM BPM VORP FG FGA FG% 3P 3PA 3P% 2P 2PA 2P% eFG% FT FTA FT% ORB
## 2 144 516 0.279 144 516 0.279 0.279 170 241 0.705
## 3 102 274 0.372 102 274 0.372 0.372 75 106 0.708
## 4 174 499 0.349 174 499 0.349 0.349 90 129 0.698
## 5 22 86 0.256 22 86 0.256 0.256 19 34 0.559
## 6 21 82 0.256 21 82 0.256 0.256 17 31 0.548
## 7 1 4 0.25 1 4 0.25 0.25 2 3 0.667
## DRB TRB AST STL BLK TOV PF PTS
## 2 176 217 458
## 3 109 99 279
## 4 140 192 438
## 5 20 29 63
## 6 20 27 59
## 7 0 2 4Let’s convert the columns into their best suited forms:
library(dplyr)
Stats <- Stats %>%
mutate(across(everything(), ~type.convert(as.character(.), as.is = TRUE)))
Stats <- Stats %>%
mutate(
Player = as.character(Player),
Pos = as.factor(Pos),
Tm = as.factor(Tm),
G = as.integer(G),
GS = as.integer(GS),
MP = as.integer(MP),
FG = as.integer(FG),
FGA = as.integer(FGA),
`3P` = as.numeric(`3P`),
`3PA` = as.numeric(`3PA`),
`2P` = as.integer(`2P`),
`2PA` = as.integer(`2PA`),
FT = as.numeric(FT),
FTA = as.numeric(FTA),
ORB = as.integer(ORB),
DRB = as.integer(DRB),
TRB = as.integer(TRB),
AST = as.integer(AST),
STL = as.integer(STL),
BLK = as.integer(BLK),
TOV = as.integer(TOV),
PF = as.integer(PF),
PTS = as.integer(PTS)
)
str(Stats)## 'data.frame': 24691 obs. of 53 variables:
## $ Sl.no : int 0 1 2 3 4 5 6 7 8 9 ...
## $ Year : int 1950 1950 1950 1950 1950 1950 1950 1950 1950 1950 ...
## $ Player: chr "Curly Armstrong" "Cliff Barker" "Leo Barnhorst" "Ed Bartels" ...
## $ Pos : Factor w/ 24 levels "","C","C-F","C-PF",..: 10 21 17 6 6 6 9 10 7 7 ...
## $ Age : int 31 29 25 24 24 24 22 23 28 28 ...
## $ Tm : Factor w/ 70 levels "","AND","ATL",..: 23 27 15 63 22 43 27 64 63 23 ...
## $ G : int 63 49 67 15 13 2 60 3 65 36 ...
## $ GS : int NA NA NA NA NA NA NA NA NA NA ...
## $ MP : int NA NA NA NA NA NA NA NA NA NA ...
## $ PER : num NA NA NA NA NA NA NA NA NA NA ...
## $ TS% : num 0.368 0.435 0.394 0.312 0.308 0.376 0.422 0.275 0.346 0.362 ...
## $ 3PAr : num NA NA NA NA NA NA NA NA NA NA ...
## $ FTr : num 0.467 0.387 0.259 0.395 0.378 0.75 0.301 0.313 0.395 0.48 ...
## $ ORB% : num NA NA NA NA NA NA NA NA NA NA ...
## $ DRB% : num NA NA NA NA NA NA NA NA NA NA ...
## $ TRB% : num NA NA NA NA NA NA NA NA NA NA ...
## $ AST% : num NA NA NA NA NA NA NA NA NA NA ...
## $ STL% : num NA NA NA NA NA NA NA NA NA NA ...
## $ BLK% : num NA NA NA NA NA NA NA NA NA NA ...
## $ TOV% : num NA NA NA NA NA NA NA NA NA NA ...
## $ USG% : num NA NA NA NA NA NA NA NA NA NA ...
## $ blank1: logi NA NA NA NA NA NA ...
## $ OWS : num -0.1 1.6 0.9 -0.5 -0.5 0 3.6 -0.1 -2.2 -0.7 ...
## $ DWS : num 3.6 0.6 2.8 -0.1 -0.1 0 1.2 0 5 2.2 ...
## $ WS : num 3.5 2.2 3.6 -0.6 -0.6 0 4.8 -0.1 2.8 1.5 ...
## $ WS/48 : num NA NA NA NA NA NA NA NA NA NA ...
## $ blank2: logi NA NA NA NA NA NA ...
## $ OBPM : num NA NA NA NA NA NA NA NA NA NA ...
## $ DBPM : num NA NA NA NA NA NA NA NA NA NA ...
## $ BPM : num NA NA NA NA NA NA NA NA NA NA ...
## $ VORP : num NA NA NA NA NA NA NA NA NA NA ...
## $ FG : int 144 102 174 22 21 1 340 5 226 125 ...
## $ FGA : int 516 274 499 86 82 4 936 16 813 435 ...
## $ FG% : num 0.279 0.372 0.349 0.256 0.256 0.25 0.363 0.313 0.278 0.287 ...
## $ 3P : num NA NA NA NA NA NA NA NA NA NA ...
## $ 3PA : num NA NA NA NA NA NA NA NA NA NA ...
## $ 3P% : num NA NA NA NA NA NA NA NA NA NA ...
## $ 2P : int 144 102 174 22 21 1 340 5 226 125 ...
## $ 2PA : int 516 274 499 86 82 4 936 16 813 435 ...
## $ 2P% : num 0.279 0.372 0.349 0.256 0.256 0.25 0.363 0.313 0.278 0.287 ...
## $ eFG% : num 0.279 0.372 0.349 0.256 0.256 0.25 0.363 0.313 0.278 0.287 ...
## $ FT : num 170 75 90 19 17 2 215 0 209 132 ...
## $ FTA : num 241 106 129 34 31 3 282 5 321 209 ...
## $ FT% : num 0.705 0.708 0.698 0.559 0.548 0.667 0.762 0 0.651 0.632 ...
## $ ORB : int NA NA NA NA NA NA NA NA NA NA ...
## $ DRB : int NA NA NA NA NA NA NA NA NA NA ...
## $ TRB : int NA NA NA NA NA NA NA NA NA NA ...
## $ AST : int 176 109 140 20 20 0 233 2 163 75 ...
## $ STL : int NA NA NA NA NA NA NA NA NA NA ...
## $ BLK : int NA NA NA NA NA NA NA NA NA NA ...
## $ TOV : int NA NA NA NA NA NA NA NA NA NA ...
## $ PF : int 217 99 192 29 27 2 132 6 273 140 ...
## $ PTS : int 458 279 438 63 59 4 895 10 661 382 ...Let’s rename and remove unwanted columns in Salary dataset:
colnames(salary_1718) <- c("Rank","Player","Team", "Salary17_18")
salary_1718 <- salary_1718[-1, ]
salary_1718 <- salary_1718[ ,-1]
head(salary_1718)## Player Team Salary17_18
## 2 Stephen Curry GSW 34682550
## 3 LeBron James CLE 33285709
## 4 Paul Millsap DEN 31269231
## 5 Gordon Hayward BOS 29727900
## 6 Blake Griffin DET 29512900
## 7 Kyle Lowry TOR 28703704Converting salary column into numeric:
salary_1718$Salary17_18 <- as.numeric(salary_1718$Salary17_18)Now let’s filter out the stats data and fetch stats of the players for 16-17 season:
stats17 <- Stats %>%
filter(Year >= 2017) %>%
select(Year:G, MP, PER, FG:PTS) %>%
distinct(Player, .keep_all = TRUE)
head(stats17)## Year Player Pos Age Tm G MP PER FG FGA FG% 3P 3PA 3P% 2P
## 1 2017 Alex Abrines SG 23 OKC 68 1055 10.1 134 341 0.393 94 247 0.381 40
## 2 2017 Quincy Acy PF 26 TOT 38 558 11.8 70 170 0.412 37 90 0.411 33
## 3 2017 Steven Adams C 23 OKC 80 2389 16.5 374 655 0.571 0 1 0.000 374
## 4 2017 Arron Afflalo SG 31 SAC 61 1580 9.0 185 420 0.440 62 151 0.411 123
## 5 2017 Alexis Ajinca C 28 NOP 39 584 12.9 89 178 0.500 0 4 0.000 89
## 6 2017 Cole Aldrich C 28 MIN 62 531 12.7 45 86 0.523 0 0 NA 45
## 2PA 2P% eFG% FT FTA FT% ORB DRB TRB AST STL BLK TOV PF PTS
## 1 94 0.426 0.531 44 49 0.898 18 68 86 40 37 8 33 114 406
## 2 80 0.413 0.521 45 60 0.750 20 95 115 18 14 15 21 67 222
## 3 654 0.572 0.571 157 257 0.611 282 333 615 86 88 78 146 195 905
## 4 269 0.457 0.514 83 93 0.892 9 116 125 78 21 7 42 104 515
## 5 174 0.511 0.500 29 40 0.725 46 131 177 12 20 22 31 77 207
## 6 86 0.523 0.523 15 22 0.682 51 107 158 25 25 23 17 85 105Merging The two data sets
stats_and_salary <- merge(stats17, salary_1718, by.x = "Player", by.y = "Player")
summary(stats_and_salary)## Player Year Pos Age Tm
## Length:442 Min. :2017 SG :97 Min. :19.00 TOT : 53
## Class :character 1st Qu.:2017 PG :92 1st Qu.:23.00 PHO : 17
## Mode :character Median :2017 C :89 Median :26.00 BOS : 16
## Mean :2017 SF :85 Mean :26.19 CHI : 16
## 3rd Qu.:2017 PF :78 3rd Qu.:29.00 MIL : 16
## Max. :2017 PF-C : 1 Max. :40.00 UTA : 16
## (Other): 0 (Other):308
## G MP PER FG
## Min. : 2.00 Min. : 9.0 Min. :-2.10 Min. : 1.0
## 1st Qu.:42.25 1st Qu.: 625.2 1st Qu.:10.20 1st Qu.: 78.5
## Median :66.00 Median :1369.5 Median :13.00 Median :185.0
## Mean :57.91 Mean :1352.3 Mean :13.64 Mean :219.5
## 3rd Qu.:76.00 3rd Qu.:2022.5 3rd Qu.:16.30 3rd Qu.:318.5
## Max. :82.00 Max. :3048.0 Max. :30.80 Max. :824.0
##
## FGA FG% 3P 3PA
## Min. : 3.0 Min. :0.1000 Min. : 0.00 Min. : 0.00
## 1st Qu.: 181.5 1st Qu.:0.4052 1st Qu.: 4.00 1st Qu.: 18.25
## Median : 416.5 Median :0.4440 Median : 40.50 Median :117.50
## Mean : 480.7 Mean :0.4507 Mean : 54.98 Mean :153.21
## 3rd Qu.: 684.0 3rd Qu.:0.4870 3rd Qu.: 90.00 3rd Qu.:252.75
## Max. :1941.0 Max. :0.7500 Max. :324.00 Max. :789.00
##
## 3P% 2P 2PA 2P%
## Min. :0.0000 Min. : 0.0 Min. : 2.0 Min. :0.000
## 1st Qu.:0.2845 1st Qu.: 55.0 1st Qu.: 110.2 1st Qu.:0.454
## Median :0.3415 Median :126.5 Median : 254.5 Median :0.491
## Mean :0.3127 Mean :164.5 Mean : 327.5 Mean :0.492
## 3rd Qu.:0.3780 3rd Qu.:227.8 3rd Qu.: 454.8 3rd Qu.:0.536
## Max. :1.0000 Max. :730.0 Max. :1421.0 Max. :1.000
## NA's :28
## eFG% FT FTA FT%
## Min. :0.1000 Min. : 0.00 Min. : 0.00 Min. :0.0000
## 1st Qu.:0.4750 1st Qu.: 29.25 1st Qu.: 39.25 1st Qu.:0.6880
## Median :0.5070 Median : 67.00 Median : 91.00 Median :0.7700
## Mean :0.5051 Mean :100.50 Mean :129.71 Mean :0.7472
## 3rd Qu.:0.5370 3rd Qu.:131.75 3rd Qu.:170.25 3rd Qu.:0.8367
## Max. :0.8750 Max. :746.00 Max. :881.00 Max. :1.0000
## NA's :4
## ORB DRB TRB AST
## Min. : 0.00 Min. : 0.00 Min. : 0.00 Min. : 0.0
## 1st Qu.: 16.00 1st Qu.: 78.25 1st Qu.: 99.25 1st Qu.: 37.0
## Median : 35.00 Median :164.00 Median : 205.50 Median : 82.0
## Mean : 55.46 Mean :186.32 Mean : 241.77 Mean :127.3
## 3rd Qu.: 75.75 3rd Qu.:252.75 3rd Qu.: 328.25 3rd Qu.:165.5
## Max. :345.00 Max. :817.00 Max. :1116.00 Max. :906.0
##
## STL BLK TOV PF
## Min. : 0.00 Min. : 0.00 Min. : 0.00 Min. : 0.0
## 1st Qu.: 18.25 1st Qu.: 7.00 1st Qu.: 31.25 1st Qu.: 61.0
## Median : 39.00 Median : 17.00 Median : 61.00 Median :114.0
## Mean : 43.28 Mean : 26.06 Mean : 75.18 Mean :110.7
## 3rd Qu.: 60.00 3rd Qu.: 33.75 3rd Qu.:106.00 3rd Qu.:153.8
## Max. :157.00 Max. :214.00 Max. :464.00 Max. :278.0
##
## PTS Team Salary17_18
## Min. : 3.0 Length:442 Min. : 17224
## 1st Qu.: 209.2 Class :character 1st Qu.: 1518316
## Median : 497.0 Mode :character Median : 3519283
## Mean : 594.5 Mean : 7106258
## 3rd Qu.: 841.2 3rd Qu.:10812701
## Max. :2558.0 Max. :34682550
## From from the summary, after merging we can see that there are few Na values to be handled.
(c) Cleaning
head(stats_and_salary)## Player Year Pos Age Tm G MP PER FG FGA FG% 3P 3PA 3P% 2P
## 1 A.J. Hammons 2017 C 24 DAL 22 163 8.4 17 42 0.405 5 10 0.500 12
## 2 Aaron Brooks 2017 PG 32 IND 65 894 9.5 121 300 0.403 48 128 0.375 73
## 3 Aaron Gordon 2017 SF 21 ORL 80 2298 14.4 393 865 0.454 77 267 0.288 316
## 4 Al-Farouq Aminu 2017 SF 26 POR 61 1773 11.3 183 466 0.393 70 212 0.330 113
## 5 Al Horford 2017 C 30 BOS 68 2193 17.7 379 801 0.473 86 242 0.355 293
## 6 Al Jefferson 2017 C 32 IND 66 931 18.9 235 471 0.499 0 1 0.000 235
## 2PA 2P% eFG% FT FTA FT% ORB DRB TRB AST STL BLK TOV PF PTS Team
## 1 32 0.375 0.464 9 20 0.450 8 28 36 4 1 13 10 21 48 MIA
## 2 172 0.424 0.483 32 40 0.800 18 51 69 125 25 9 66 93 322 MIN
## 3 598 0.528 0.499 156 217 0.719 116 289 405 150 64 40 89 172 1019 ORL
## 4 254 0.445 0.468 96 136 0.706 77 374 451 99 60 44 94 102 532 POR
## 5 559 0.524 0.527 108 135 0.800 95 369 464 337 52 87 116 138 952 BOS
## 6 470 0.500 0.499 65 85 0.765 75 203 278 57 19 16 33 125 535 IND
## Salary17_18
## 1 1312611
## 2 2116955
## 3 5504420
## 4 7319035
## 5 27734405
## 6 9769821Here we can remove the Team column from the stats_and_salary data as it is not required for analysis. This column indicates the team to which the player belonged in 17-18 season, Which is not required for us.
library(dplyr)
stats_and_salary <- stats_and_salary %>% select(-Team)Now let’s check the summary and also check if there are any Na values in our merged dataset.
summary(stats_and_salary)## Player Year Pos Age Tm
## Length:442 Min. :2017 SG :97 Min. :19.00 TOT : 53
## Class :character 1st Qu.:2017 PG :92 1st Qu.:23.00 PHO : 17
## Mode :character Median :2017 C :89 Median :26.00 BOS : 16
## Mean :2017 SF :85 Mean :26.19 CHI : 16
## 3rd Qu.:2017 PF :78 3rd Qu.:29.00 MIL : 16
## Max. :2017 PF-C : 1 Max. :40.00 UTA : 16
## (Other): 0 (Other):308
## G MP PER FG
## Min. : 2.00 Min. : 9.0 Min. :-2.10 Min. : 1.0
## 1st Qu.:42.25 1st Qu.: 625.2 1st Qu.:10.20 1st Qu.: 78.5
## Median :66.00 Median :1369.5 Median :13.00 Median :185.0
## Mean :57.91 Mean :1352.3 Mean :13.64 Mean :219.5
## 3rd Qu.:76.00 3rd Qu.:2022.5 3rd Qu.:16.30 3rd Qu.:318.5
## Max. :82.00 Max. :3048.0 Max. :30.80 Max. :824.0
##
## FGA FG% 3P 3PA
## Min. : 3.0 Min. :0.1000 Min. : 0.00 Min. : 0.00
## 1st Qu.: 181.5 1st Qu.:0.4052 1st Qu.: 4.00 1st Qu.: 18.25
## Median : 416.5 Median :0.4440 Median : 40.50 Median :117.50
## Mean : 480.7 Mean :0.4507 Mean : 54.98 Mean :153.21
## 3rd Qu.: 684.0 3rd Qu.:0.4870 3rd Qu.: 90.00 3rd Qu.:252.75
## Max. :1941.0 Max. :0.7500 Max. :324.00 Max. :789.00
##
## 3P% 2P 2PA 2P%
## Min. :0.0000 Min. : 0.0 Min. : 2.0 Min. :0.000
## 1st Qu.:0.2845 1st Qu.: 55.0 1st Qu.: 110.2 1st Qu.:0.454
## Median :0.3415 Median :126.5 Median : 254.5 Median :0.491
## Mean :0.3127 Mean :164.5 Mean : 327.5 Mean :0.492
## 3rd Qu.:0.3780 3rd Qu.:227.8 3rd Qu.: 454.8 3rd Qu.:0.536
## Max. :1.0000 Max. :730.0 Max. :1421.0 Max. :1.000
## NA's :28
## eFG% FT FTA FT%
## Min. :0.1000 Min. : 0.00 Min. : 0.00 Min. :0.0000
## 1st Qu.:0.4750 1st Qu.: 29.25 1st Qu.: 39.25 1st Qu.:0.6880
## Median :0.5070 Median : 67.00 Median : 91.00 Median :0.7700
## Mean :0.5051 Mean :100.50 Mean :129.71 Mean :0.7472
## 3rd Qu.:0.5370 3rd Qu.:131.75 3rd Qu.:170.25 3rd Qu.:0.8367
## Max. :0.8750 Max. :746.00 Max. :881.00 Max. :1.0000
## NA's :4
## ORB DRB TRB AST
## Min. : 0.00 Min. : 0.00 Min. : 0.00 Min. : 0.0
## 1st Qu.: 16.00 1st Qu.: 78.25 1st Qu.: 99.25 1st Qu.: 37.0
## Median : 35.00 Median :164.00 Median : 205.50 Median : 82.0
## Mean : 55.46 Mean :186.32 Mean : 241.77 Mean :127.3
## 3rd Qu.: 75.75 3rd Qu.:252.75 3rd Qu.: 328.25 3rd Qu.:165.5
## Max. :345.00 Max. :817.00 Max. :1116.00 Max. :906.0
##
## STL BLK TOV PF
## Min. : 0.00 Min. : 0.00 Min. : 0.00 Min. : 0.0
## 1st Qu.: 18.25 1st Qu.: 7.00 1st Qu.: 31.25 1st Qu.: 61.0
## Median : 39.00 Median : 17.00 Median : 61.00 Median :114.0
## Mean : 43.28 Mean : 26.06 Mean : 75.18 Mean :110.7
## 3rd Qu.: 60.00 3rd Qu.: 33.75 3rd Qu.:106.00 3rd Qu.:153.8
## Max. :157.00 Max. :214.00 Max. :464.00 Max. :278.0
##
## PTS Salary17_18
## Min. : 3.0 Min. : 17224
## 1st Qu.: 209.2 1st Qu.: 1518316
## Median : 497.0 Median : 3519283
## Mean : 594.5 Mean : 7106258
## 3rd Qu.: 841.2 3rd Qu.:10812701
## Max. :2558.0 Max. :34682550
## sum(is.na(stats_and_salary))## [1] 32our Merged data has 32 Na values in total to be handled. We can replace these Na values by the means of their columns.I chose this approach because, since it is a sports data containing stats of each player, we cannot omit an entire player’s data because of just few missing values.
numeric_cols <- sapply(stats_and_salary, is.numeric)
stats_and_salary[, numeric_cols] <-
lapply(stats_and_salary[, numeric_cols],
function(col) ifelse(is.na(col), mean(col, na.rm = TRUE), col))
sum(is.na(stats_and_salary))## [1] 0summary(stats_and_salary)## Player Year Pos Age Tm
## Length:442 Min. :2017 SG :97 Min. :19.00 TOT : 53
## Class :character 1st Qu.:2017 PG :92 1st Qu.:23.00 PHO : 17
## Mode :character Median :2017 C :89 Median :26.00 BOS : 16
## Mean :2017 SF :85 Mean :26.19 CHI : 16
## 3rd Qu.:2017 PF :78 3rd Qu.:29.00 MIL : 16
## Max. :2017 PF-C : 1 Max. :40.00 UTA : 16
## (Other): 0 (Other):308
## G MP PER FG
## Min. : 2.00 Min. : 9.0 Min. :-2.10 Min. : 1.0
## 1st Qu.:42.25 1st Qu.: 625.2 1st Qu.:10.20 1st Qu.: 78.5
## Median :66.00 Median :1369.5 Median :13.00 Median :185.0
## Mean :57.91 Mean :1352.3 Mean :13.64 Mean :219.5
## 3rd Qu.:76.00 3rd Qu.:2022.5 3rd Qu.:16.30 3rd Qu.:318.5
## Max. :82.00 Max. :3048.0 Max. :30.80 Max. :824.0
##
## FGA FG% 3P 3PA
## Min. : 3.0 Min. :0.1000 Min. : 0.00 Min. : 0.00
## 1st Qu.: 181.5 1st Qu.:0.4052 1st Qu.: 4.00 1st Qu.: 18.25
## Median : 416.5 Median :0.4440 Median : 40.50 Median :117.50
## Mean : 480.7 Mean :0.4507 Mean : 54.98 Mean :153.21
## 3rd Qu.: 684.0 3rd Qu.:0.4870 3rd Qu.: 90.00 3rd Qu.:252.75
## Max. :1941.0 Max. :0.7500 Max. :324.00 Max. :789.00
##
## 3P% 2P 2PA 2P%
## Min. :0.0000 Min. : 0.0 Min. : 2.0 Min. :0.000
## 1st Qu.:0.2900 1st Qu.: 55.0 1st Qu.: 110.2 1st Qu.:0.454
## Median :0.3360 Median :126.5 Median : 254.5 Median :0.491
## Mean :0.3127 Mean :164.5 Mean : 327.5 Mean :0.492
## 3rd Qu.:0.3750 3rd Qu.:227.8 3rd Qu.: 454.8 3rd Qu.:0.536
## Max. :1.0000 Max. :730.0 Max. :1421.0 Max. :1.000
##
## eFG% FT FTA FT%
## Min. :0.1000 Min. : 0.00 Min. : 0.00 Min. :0.0000
## 1st Qu.:0.4750 1st Qu.: 29.25 1st Qu.: 39.25 1st Qu.:0.6880
## Median :0.5070 Median : 67.00 Median : 91.00 Median :0.7695
## Mean :0.5051 Mean :100.50 Mean :129.71 Mean :0.7472
## 3rd Qu.:0.5370 3rd Qu.:131.75 3rd Qu.:170.25 3rd Qu.:0.8353
## Max. :0.8750 Max. :746.00 Max. :881.00 Max. :1.0000
##
## ORB DRB TRB AST
## Min. : 0.00 Min. : 0.00 Min. : 0.00 Min. : 0.0
## 1st Qu.: 16.00 1st Qu.: 78.25 1st Qu.: 99.25 1st Qu.: 37.0
## Median : 35.00 Median :164.00 Median : 205.50 Median : 82.0
## Mean : 55.46 Mean :186.32 Mean : 241.77 Mean :127.3
## 3rd Qu.: 75.75 3rd Qu.:252.75 3rd Qu.: 328.25 3rd Qu.:165.5
## Max. :345.00 Max. :817.00 Max. :1116.00 Max. :906.0
##
## STL BLK TOV PF
## Min. : 0.00 Min. : 0.00 Min. : 0.00 Min. : 0.0
## 1st Qu.: 18.25 1st Qu.: 7.00 1st Qu.: 31.25 1st Qu.: 61.0
## Median : 39.00 Median : 17.00 Median : 61.00 Median :114.0
## Mean : 43.28 Mean : 26.06 Mean : 75.18 Mean :110.7
## 3rd Qu.: 60.00 3rd Qu.: 33.75 3rd Qu.:106.00 3rd Qu.:153.8
## Max. :157.00 Max. :214.00 Max. :464.00 Max. :278.0
##
## PTS Salary17_18
## Min. : 3.0 Min. : 17224
## 1st Qu.: 209.2 1st Qu.: 1518316
## Median : 497.0 Median : 3519283
## Mean : 594.5 Mean : 7106258
## 3rd Qu.: 841.2 3rd Qu.:10812701
## Max. :2558.0 Max. :34682550
## b.Data Exploration
Per-Game stats:
The original dataset includes whole-season statistics (e.g., total points, total assists) for each player. However, these cumulative totals can be misleading when comparing players who played different numbers of games.
Per-game statistics provide a more accurate representation of a player’s average performance, making comparisons fairer.
Some players may not play the entire season due to injuries, resting, or other factors. As a result, their cumulative season totals could appear lower, even if they have strong performances when they are on the court.
By calculating per-game statistics (e.g., PPG - Points Per Game, MPG - Minutes Per Game), we normalize the data to reflect a player’s contribution in each game they play, rather than across an entire season.
Creation of Per-Game Statistics
The dataset originally contained cumulative season totals (e.g., total points, total minutes played)
MPG (Minutes Per Game): MP/G
PPG (Points Per Game): PTS/G
APG (Assists Per Game): AST/G
RPG (Rebounds Per Game): TRB/G
TOPG (Turnovers Per Game): TOV/G
BPG (Blocks Per Game): BLK/G
SPG (Steals Per Game): STL/G
stats_and_salary <- stats_and_salary %>%
mutate(MPG = MP / G, PPG = PTS / G, APG = AST / G,
RPG = TRB / G, TOPG = TOV / G, BPG = BLK / G,
SPG = STL / G)
head(stats_and_salary)## Player Year Pos Age Tm G MP PER FG FGA FG% 3P 3PA 3P% 2P
## 1 A.J. Hammons 2017 C 24 DAL 22 163 8.4 17 42 0.405 5 10 0.500 12
## 2 Aaron Brooks 2017 PG 32 IND 65 894 9.5 121 300 0.403 48 128 0.375 73
## 3 Aaron Gordon 2017 SF 21 ORL 80 2298 14.4 393 865 0.454 77 267 0.288 316
## 4 Al-Farouq Aminu 2017 SF 26 POR 61 1773 11.3 183 466 0.393 70 212 0.330 113
## 5 Al Horford 2017 C 30 BOS 68 2193 17.7 379 801 0.473 86 242 0.355 293
## 6 Al Jefferson 2017 C 32 IND 66 931 18.9 235 471 0.499 0 1 0.000 235
## 2PA 2P% eFG% FT FTA FT% ORB DRB TRB AST STL BLK TOV PF PTS
## 1 32 0.375 0.464 9 20 0.450 8 28 36 4 1 13 10 21 48
## 2 172 0.424 0.483 32 40 0.800 18 51 69 125 25 9 66 93 322
## 3 598 0.528 0.499 156 217 0.719 116 289 405 150 64 40 89 172 1019
## 4 254 0.445 0.468 96 136 0.706 77 374 451 99 60 44 94 102 532
## 5 559 0.524 0.527 108 135 0.800 95 369 464 337 52 87 116 138 952
## 6 470 0.500 0.499 65 85 0.765 75 203 278 57 19 16 33 125 535
## Salary17_18 MPG PPG APG RPG TOPG BPG
## 1 1312611 7.409091 2.181818 0.1818182 1.636364 0.4545455 0.5909091
## 2 2116955 13.753846 4.953846 1.9230769 1.061538 1.0153846 0.1384615
## 3 5504420 28.725000 12.737500 1.8750000 5.062500 1.1125000 0.5000000
## 4 7319035 29.065574 8.721311 1.6229508 7.393443 1.5409836 0.7213115
## 5 27734405 32.250000 14.000000 4.9558824 6.823529 1.7058824 1.2794118
## 6 9769821 14.106061 8.106061 0.8636364 4.212121 0.5000000 0.2424242
## SPG
## 1 0.04545455
## 2 0.38461538
## 3 0.80000000
## 4 0.98360656
## 5 0.76470588
## 6 0.28787879Now we can only keep our per-game stats for analysis by removing the cumulative stats of the player for entire season.
per_game_stats <- stats_and_salary %>% select(Player, Tm, MPG, PPG, APG, RPG, TOPG, BPG, SPG, Salary17_18)
head(per_game_stats)## Player Tm MPG PPG APG RPG TOPG
## 1 A.J. Hammons DAL 7.409091 2.181818 0.1818182 1.636364 0.4545455
## 2 Aaron Brooks IND 13.753846 4.953846 1.9230769 1.061538 1.0153846
## 3 Aaron Gordon ORL 28.725000 12.737500 1.8750000 5.062500 1.1125000
## 4 Al-Farouq Aminu POR 29.065574 8.721311 1.6229508 7.393443 1.5409836
## 5 Al Horford BOS 32.250000 14.000000 4.9558824 6.823529 1.7058824
## 6 Al Jefferson IND 14.106061 8.106061 0.8636364 4.212121 0.5000000
## BPG SPG Salary17_18
## 1 0.5909091 0.04545455 1312611
## 2 0.1384615 0.38461538 2116955
## 3 0.5000000 0.80000000 5504420
## 4 0.7213115 0.98360656 7319035
## 5 1.2794118 0.76470588 27734405
## 6 0.2424242 0.28787879 9769821correlation-1
library(corrplot)## corrplot 0.95 loadedlibrary(dplyr)
numeric_columns <- per_game_stats %>%
select(MPG, PPG, APG, RPG, TOPG, BPG, SPG, Salary17_18)
cor_matrix <- cor(numeric_columns, use = "complete.obs")
corrplot(cor_matrix,
method = "circle",
type = "upper",
tl.col = "black",
tl.srt = 45,
title = "Correlation Plot for Salary and Stats",
mar = c(0, 0, 1, 0)) 
Correlation-2
library(dplyr)
library(GGally)## Loading required package: ggplot2## Registered S3 method overwritten by 'GGally':
## method from
## +.gg ggplot2stats_salary_cor <-
per_game_stats %>%
select(Salary17_18, PPG, MPG, TOPG, RPG, SPG, APG)
ggpairs(stats_salary_cor)
By observing these two plots:
The Strength of correlation between the variables is ranked as follows: PPG>MPG>TOPG>RPG>PER>SPG>APG
The number of turnovers (TOPG) made by players shows a positive correlation with their salary. We interpreted this as: “The more turnovers a player makes, the more involved they are in ball movements during the game.“
This could suggest that players who make turnovers might be more important to their team, possibly due to their aggressive playstyle.
We realize that this interpretation may not be fully accurate. For more precise analysis, we should consider additional data, such as how long each player holds the ball during games.
Let’s visualize a scatter plot between PPG and salary as they are highly correlated.
library(dplyr)
per_game_stats <- per_game_stats %>%
rename(Team = Tm)library(plotly)##
## Attaching package: 'plotly'## The following object is masked from 'package:ggplot2':
##
## last_plot## The following object is masked from 'package:stats':
##
## filter## The following object is masked from 'package:graphics':
##
## layoutplot_ly(data = per_game_stats, x = ~Salary17_18, y = ~PPG, color = ~Team,
hoverinfo = "text",
text = ~paste("Player: ", Player,
"<br>Salary: ", format(Salary17_18, big.mark = ","),"$",
"<br>PPG: ", round(PPG, digits = 3),
"<br>Team: ", Team)) %>%
layout(
title = "Salary vs Point Per Game",
xaxis = list(title = "Salary USD"),
yaxis = list(title = "Point per Game")
)## No trace type specified:
## Based on info supplied, a 'scatter' trace seems appropriate.
## Read more about this trace type -> https://plotly.com/r/reference/#scatter## No scatter mode specifed:
## Setting the mode to markers
## Read more about this attribute -> https://plotly.com/r/reference/#scatter-mode## Warning in RColorBrewer::brewer.pal(N, "Set2"): n too large, allowed maximum for palette Set2 is 8
## Returning the palette you asked for with that many colors
## Warning in RColorBrewer::brewer.pal(N, "Set2"): n too large, allowed maximum for palette Set2 is 8
## Returning the palette you asked for with that many colorsIf you hover on the points in this plot, you can check the player names. As you can tell the most paid player is Stephen Curry.
Linear regression:
library(ggplot2)
per_game_stats %>%
ggplot(aes(x = Salary17_18, y = PPG)) +
geom_point() +
geom_smooth(method = "lm") ## `geom_smooth()` using formula = 'y ~ x'
You can see a general upward trend, which means that as players score more points per game, their salaries tend to be higher.
The blue line is a trend line that shows this overall pattern, and the shaded area around it represents the range where most data points are likely to fall, showing confidence in this trend.
In simple terms, players who score more points usually earn higher salaries.
stats_salary_regression <-
per_game_stats %>% select(Salary17_18, MPG:SPG)
lm(Salary17_18~., data=stats_salary_regression)##
## Call:
## lm(formula = Salary17_18 ~ ., data = stats_salary_regression)
##
## Coefficients:
## (Intercept) MPG PPG APG RPG TOPG
## -2792909 30565 686815 1059087 916087 -2709447
## BPG SPG
## 470136 631255Scoring points, assisting, and rebounding contribute the most to higher salaries. Turnovers (losing possession) have a large negative impact on salary.
Defensive stats like blocks and steals also contribute positively but to a lesser extent than scoring and playmaking skills.
d. Data Preprocessing
Earlier in Correlation analysis we saw that even turnovers have a bit of positive impact over a player’s salary and we related it to a player’s aggressive playstyle, if a player is involved more in ball movements he tends to commit turn overs, so here we can a create a variable called as Aggressiveness.
If a player’s turnovers per game are equal to or above this average, they’re labeled as “Yes” for Aggressiveness (meaning they turn over the ball relatively often).
Apart from this we can also observe that MPG (minutes per game) also have a positive relation with the salary. Players who generally trusted by their coaches tend to play more on court and tend to score more which boosts their salaries, Hence we can create another variable called Trusted.
If a player’s minutes per game are equal to or above this average, they’re labeled as “Yes” for Trust (meaning the coach plays them often, indicating trust).
avg.minutes <- mean(per_game_stats$MPG)
avg.turnover <- mean(per_game_stats$TOPG)
per_game_stats$Trusted <- as.factor(ifelse(per_game_stats$MPG >= avg.minutes, "Yes", "No"))
per_game_stats$Agressiveness <- as.factor(ifelse(per_game_stats$TOPG >= avg.turnover, "Yes", "No"))
head(per_game_stats)## Player Team MPG PPG APG RPG TOPG
## 1 A.J. Hammons DAL 7.409091 2.181818 0.1818182 1.636364 0.4545455
## 2 Aaron Brooks IND 13.753846 4.953846 1.9230769 1.061538 1.0153846
## 3 Aaron Gordon ORL 28.725000 12.737500 1.8750000 5.062500 1.1125000
## 4 Al-Farouq Aminu POR 29.065574 8.721311 1.6229508 7.393443 1.5409836
## 5 Al Horford BOS 32.250000 14.000000 4.9558824 6.823529 1.7058824
## 6 Al Jefferson IND 14.106061 8.106061 0.8636364 4.212121 0.5000000
## BPG SPG Salary17_18 Trusted Agressiveness
## 1 0.5909091 0.04545455 1312611 No No
## 2 0.1384615 0.38461538 2116955 No No
## 3 0.5000000 0.80000000 5504420 Yes No
## 4 0.7213115 0.98360656 7319035 Yes Yes
## 5 1.2794118 0.76470588 27734405 Yes Yes
## 6 0.2424242 0.28787879 9769821 No Noper_game_stats %>%
ggplot(aes(x = Salary17_18, y = PPG, colour = Agressiveness)) +
geom_point() +
geom_smooth(method="lm")## `geom_smooth()` using formula = 'y ~ x'
The data points are color-coded by “Aggressiveness,” which is based on whether the player has an above-average or below-average number of turnovers (TOPG).
Here, players labeled “Yes” in teal have higher turnovers (more aggressive), while players labeled “No” in red have fewer turnovers. The trend lines for each group show the general relationship between salary and points per game for players with different levels of aggressiveness.
Positive Salary-Performance Trend: As salary increases, players generally score more points per game, which indicates that higher-paid players tend to perform better in terms of scoring.
Aggressiveness Impact: The teal line (for aggressive players) is above the red line, suggesting that players who are more aggressive (higher turnovers) tend to have slightly higher PPG at a given salary level compared to less aggressive players.
per_game_stats$TrustedYes <- ifelse(per_game_stats$Trusted == "Yes", 1, 0)
per_game_stats$AgressivenessYes <- ifelse(per_game_stats$Agressiveness == "Yes", 1, 0)
head(per_game_stats)## Player Team MPG PPG APG RPG TOPG
## 1 A.J. Hammons DAL 7.409091 2.181818 0.1818182 1.636364 0.4545455
## 2 Aaron Brooks IND 13.753846 4.953846 1.9230769 1.061538 1.0153846
## 3 Aaron Gordon ORL 28.725000 12.737500 1.8750000 5.062500 1.1125000
## 4 Al-Farouq Aminu POR 29.065574 8.721311 1.6229508 7.393443 1.5409836
## 5 Al Horford BOS 32.250000 14.000000 4.9558824 6.823529 1.7058824
## 6 Al Jefferson IND 14.106061 8.106061 0.8636364 4.212121 0.5000000
## BPG SPG Salary17_18 Trusted Agressiveness TrustedYes
## 1 0.5909091 0.04545455 1312611 No No 0
## 2 0.1384615 0.38461538 2116955 No No 0
## 3 0.5000000 0.80000000 5504420 Yes No 1
## 4 0.7213115 0.98360656 7319035 Yes Yes 1
## 5 1.2794118 0.76470588 27734405 Yes Yes 1
## 6 0.2424242 0.28787879 9769821 No No 0
## AgressivenessYes
## 1 0
## 2 0
## 3 0
## 4 1
## 5 1
## 6 0library(dplyr)
per_game_stats <- per_game_stats %>% select(-Trusted, -Agressiveness)
head(per_game_stats)## Player Team MPG PPG APG RPG TOPG
## 1 A.J. Hammons DAL 7.409091 2.181818 0.1818182 1.636364 0.4545455
## 2 Aaron Brooks IND 13.753846 4.953846 1.9230769 1.061538 1.0153846
## 3 Aaron Gordon ORL 28.725000 12.737500 1.8750000 5.062500 1.1125000
## 4 Al-Farouq Aminu POR 29.065574 8.721311 1.6229508 7.393443 1.5409836
## 5 Al Horford BOS 32.250000 14.000000 4.9558824 6.823529 1.7058824
## 6 Al Jefferson IND 14.106061 8.106061 0.8636364 4.212121 0.5000000
## BPG SPG Salary17_18 TrustedYes AgressivenessYes
## 1 0.5909091 0.04545455 1312611 0 0
## 2 0.1384615 0.38461538 2116955 0 0
## 3 0.5000000 0.80000000 5504420 1 0
## 4 0.7213115 0.98360656 7319035 1 1
## 5 1.2794118 0.76470588 27734405 1 1
## 6 0.2424242 0.28787879 9769821 0 0Let’s re arrange the columns in a proper order.
library(dplyr)
per_game_stats <- per_game_stats %>%
select(Player, Team, MPG, PPG, APG, RPG, TOPG, BPG, SPG, TrustedYes, AgressivenessYes, Salary17_18)
head(per_game_stats)## Player Team MPG PPG APG RPG TOPG
## 1 A.J. Hammons DAL 7.409091 2.181818 0.1818182 1.636364 0.4545455
## 2 Aaron Brooks IND 13.753846 4.953846 1.9230769 1.061538 1.0153846
## 3 Aaron Gordon ORL 28.725000 12.737500 1.8750000 5.062500 1.1125000
## 4 Al-Farouq Aminu POR 29.065574 8.721311 1.6229508 7.393443 1.5409836
## 5 Al Horford BOS 32.250000 14.000000 4.9558824 6.823529 1.7058824
## 6 Al Jefferson IND 14.106061 8.106061 0.8636364 4.212121 0.5000000
## BPG SPG TrustedYes AgressivenessYes Salary17_18
## 1 0.5909091 0.04545455 0 0 1312611
## 2 0.1384615 0.38461538 0 0 2116955
## 3 0.5000000 0.80000000 1 0 5504420
## 4 0.7213115 0.98360656 1 1 7319035
## 5 1.2794118 0.76470588 1 1 27734405
## 6 0.2424242 0.28787879 0 0 9769821The dataset appears clean and does not require extensive preprocessing. Player statistics such as PPG, MPG, and other performance metrics are inherently meaningful and directly interpretable in their current form, making scaling unnecessary. These values represent individual player performances, and altering them would distort their real-world significance.
Additionally, there are no apparent missing values or extreme outliers based on the summary statistics, indicating that the data is ready for analysis without major cleaning. However, as part of preprocessing, dummy variables will be created for categorical variables like Trusted and Aggressiveness to ensure compatibility with machine learning models that require numerical inputs.
####e.Clustering
Pre-processing
We can exclude non numeric data for clustering like, team, Player, etc
data_for_clustering <- per_game_stats %>%
select(MPG, PPG, APG, RPG, TOPG, BPG, SPG, TrustedYes, AgressivenessYes, Salary17_18)Determining the optimal number of clusters
1.Elbow Method
library(ggplot2)
library(factoextra)## Welcome! Want to learn more? See two factoextra-related books at https://goo.gl/ve3WBaset.seed(123)
wss <- sapply(1:10, function(k) {
kmeans(data_for_clustering, centers = k, nstart = 25)$tot.withinss
})
ggplot(data.frame(k = 1:10, wss = wss), aes(x = k, y = wss)) +
geom_line() +
geom_point() +
labs(title = "Elbow Method for Determining Optimal Clusters", x = "Number of Clusters", y = "Within-cluster Sum of Squares")
The optimal number of clusters appears to be 3. This is because the WSS continues to decrease after k=3, but the reduction become less steep at k = 3, indicating adding more clusters does not improve the clustering significantly.
2.Silhouette Method:
library(cluster)
sil_scores <- sapply(2:10, function(k) {
km <- kmeans(data_for_clustering, centers = k, nstart = 25)
silhouette(km$cluster, dist(data_for_clustering))[, 3]
})
sil_plot <- ggplot(data.frame(k = 2:10, silhouette = sapply(sil_scores, mean)), aes(x = k, y = silhouette)) +
geom_line() + geom_point() +
labs(title = "Silhouette Method for Optimal Clusters", x = "Number of Clusters", y = "Average Silhouette Score")
print(sil_plot)
Here we can observe that, 3 is the optimal number of clusters as it has the highest Average Silhouette Score.
f.Clustering
set.seed(123)
kmeans_result <- kmeans(data_for_clustering, centers = 3, nstart = 25)
per_game_stats$Cluster <- as.factor(kmeans_result$cluster)Now let’s visualize the clusters with PCA.
library(ggplot2)
library(FactoMineR)
pca_result <- prcomp(data_for_clustering, scale. = TRUE)
pca_df <- data.frame(pca_result$x, Cluster = as.factor(kmeans_result$cluster))
ggplot(pca_df, aes(x = PC1, y = PC2, color = Cluster)) +
geom_point(size = 3) +
labs(title = "PCA Projection of Clustering Results", x = "PC1", y = "PC2") +
theme_minimal()
observations:
Cluster 1 (RED) seems to form a more compact group
Cluster 2 (GREEN) shows a more spread out group
Cluster 3 (Blue) is more separated and spread, indicating that the players in this cluster may have a different set of characteristics compared to the others.
table(per_game_stats$Cluster, per_game_stats$TrustedYes)##
## 0 1
## 1 16 79
## 2 205 95
## 3 1 46This table shows how the variable TrustedYes is distributed across the different clusters.
Cluster 1 has 16 players with TrustedYes = 0 and 70 with TrustedYes = 1, indicating that most of the players in this cluster are trusted by their coach
Cluster 2 has 205 players with TrustedYes = 0 and 95 with TrustedYes = 1, indicating that this cluster has a higher number of non-trusted players.
Cluster 3 has 1 players with TrustedYes = 0 and 46 with TrustedYes = 1, indicating that this cluster has almost entirely trusted players.
This suggests that cluster 3 may be the cluster most associated with trusted players, while cluster 2 contains a more balanced mix, and cluster 1 is skewed towards trusted players.
table(per_game_stats$Cluster, per_game_stats$AgressivenessYes)##
## 0 1
## 1 40 55
## 2 220 80
## 3 4 43This table shows how the variable AgressivenessYes is distributed across the different clusters.
Cluster 1 has 40 players with AgressivenessYes = 0 and 55 players with AgressivenessYes = 1, showing a fairly balanced distribution.
cluster 2 has 220 players with AgressivenessYes = 0 and 80 with AgressivenessYes = 1, indicating that this cluster has a higher number of non-aggressive players.
cluster 3 has a 4 players with AgressivenessYes = 0 and 43 with AgressivenessYes = 1, suggesting that it contains a high proportion of aggressive players.
Cluster 3 has the most aggressive players, while cluster 2 has a higher proportion of non-aggressive players.
stats_salary_regression <-
per_game_stats %>% select(MPG, PPG, APG, RPG, TOPG, BPG, SPG, TrustedYes,AgressivenessYes, Salary17_18 )
lm(Salary17_18~ TrustedYes * AgressivenessYes, data=stats_salary_regression)##
## Call:
## lm(formula = Salary17_18 ~ TrustedYes * AgressivenessYes, data = stats_salary_regression)
##
## Coefficients:
## (Intercept) TrustedYes
## 2914582 5125780
## AgressivenessYes TrustedYes:AgressivenessYes
## 969783 3518647Intercept (2,914,582): This is the baseline salary for a player who is neither trusted nor aggressive.
TrustedYes (5,125,780): Players trusted by the coach (i.e., those who play more minutes) earn significantly more, even when adjusting for other factors.
AggressivenessYes (969,783): More aggressive players (those with higher turnovers) also have a slight salary increase.
TrustedYes(3,518,647): When a player is both trusted and aggressive, their salary further increases significantly.
Players who are both trusted by their coach (play more minutes) and play aggressively (higher turnovers) tend to have higher salaries. The trend lines in the plot confirm that aggressive players tend to score more points per game at similar salary levels.
f. Classification
stepwise model:
Here let’s include all the variables, second order terms and interaction terms in the model and then perform stepwise regression to identify which combination comes out as the best ones.
library(caret)## Loading required package: latticemodel2 <- lm(Salary17_18 ~ (MPG + PPG + APG + RPG + TOPG + BPG + SPG + TrustedYes + AgressivenessYes)^2 +
I(MPG^2) + I(PPG^2) + I(APG^2) + I(RPG^2) + I(TOPG^2) + I(BPG^2) + I(SPG^2) +
I(TrustedYes^2) + I(AgressivenessYes^2), data = per_game_stats,trControl = train_control)## Warning: In lm.fit(x, y, offset = offset, singular.ok = singular.ok, ...) :
## extra argument 'trControl' will be disregardedmodel_stepwise <- step(model2, direction = "both", trace = 1)## Start: AIC=13668.5
## Salary17_18 ~ (MPG + PPG + APG + RPG + TOPG + BPG + SPG + TrustedYes +
## AgressivenessYes)^2 + I(MPG^2) + I(PPG^2) + I(APG^2) + I(RPG^2) +
## I(TOPG^2) + I(BPG^2) + I(SPG^2) + I(TrustedYes^2) + I(AgressivenessYes^2)## Warning: In lm.fit(x, y, offset = offset, singular.ok = singular.ok, ...) :
## extra argument 'trControl' will be disregarded##
## Step: AIC=13668.5
## Salary17_18 ~ MPG + PPG + APG + RPG + TOPG + BPG + SPG + TrustedYes +
## AgressivenessYes + I(MPG^2) + I(PPG^2) + I(APG^2) + I(RPG^2) +
## I(TOPG^2) + I(BPG^2) + I(SPG^2) + I(TrustedYes^2) + MPG:PPG +
## MPG:APG + MPG:RPG + MPG:TOPG + MPG:BPG + MPG:SPG + MPG:TrustedYes +
## MPG:AgressivenessYes + PPG:APG + PPG:RPG + PPG:TOPG + PPG:BPG +
## PPG:SPG + PPG:TrustedYes + PPG:AgressivenessYes + APG:RPG +
## APG:TOPG + APG:BPG + APG:SPG + APG:TrustedYes + APG:AgressivenessYes +
## RPG:TOPG + RPG:BPG + RPG:SPG + RPG:TrustedYes + RPG:AgressivenessYes +
## TOPG:BPG + TOPG:SPG + TOPG:TrustedYes + TOPG:AgressivenessYes +
## BPG:SPG + BPG:TrustedYes + BPG:AgressivenessYes + SPG:TrustedYes +
## SPG:AgressivenessYes + TrustedYes:AgressivenessYes## Warning: In lm.fit(x, y, offset = offset, singular.ok = singular.ok, ...) :
## extra argument 'trControl' will be disregarded##
## Step: AIC=13668.5
## Salary17_18 ~ MPG + PPG + APG + RPG + TOPG + BPG + SPG + TrustedYes +
## AgressivenessYes + I(MPG^2) + I(PPG^2) + I(APG^2) + I(RPG^2) +
## I(TOPG^2) + I(BPG^2) + I(SPG^2) + MPG:PPG + MPG:APG + MPG:RPG +
## MPG:TOPG + MPG:BPG + MPG:SPG + MPG:TrustedYes + MPG:AgressivenessYes +
## PPG:APG + PPG:RPG + PPG:TOPG + PPG:BPG + PPG:SPG + PPG:TrustedYes +
## PPG:AgressivenessYes + APG:RPG + APG:TOPG + APG:BPG + APG:SPG +
## APG:TrustedYes + APG:AgressivenessYes + RPG:TOPG + RPG:BPG +
## RPG:SPG + RPG:TrustedYes + RPG:AgressivenessYes + TOPG:BPG +
## TOPG:SPG + TOPG:TrustedYes + TOPG:AgressivenessYes + BPG:SPG +
## BPG:TrustedYes + BPG:AgressivenessYes + SPG:TrustedYes +
## SPG:AgressivenessYes + TrustedYes:AgressivenessYes
##
## Df Sum of Sq RSS AIC
## - MPG:RPG 1 1.5015e+10 9.3645e+15 13666
## - APG:RPG 1 2.8404e+10 9.3645e+15 13666
## - PPG:TrustedYes 1 1.3977e+11 9.3646e+15 13666
## - MPG:PPG 1 2.3557e+11 9.3647e+15 13666
## - TOPG:TrustedYes 1 2.9463e+11 9.3648e+15 13666
## - RPG:TOPG 1 3.3107e+11 9.3648e+15 13666
## - PPG:APG 1 3.4344e+11 9.3648e+15 13666
## - APG:TOPG 1 4.8873e+11 9.3650e+15 13666
## - APG:BPG 1 1.1574e+12 9.3657e+15 13667
## - I(TOPG^2) 1 1.3109e+12 9.3658e+15 13667
## - I(MPG^2) 1 1.3810e+12 9.3659e+15 13667
## - RPG:AgressivenessYes 1 1.7359e+12 9.3662e+15 13667
## - TOPG:AgressivenessYes 1 2.3868e+12 9.3669e+15 13667
## - MPG:TOPG 1 2.7048e+12 9.3672e+15 13667
## - I(RPG^2) 1 2.7343e+12 9.3672e+15 13667
## - I(PPG^2) 1 3.9300e+12 9.3684e+15 13667
## - PPG:RPG 1 4.7660e+12 9.3693e+15 13667
## - RPG:BPG 1 6.3516e+12 9.3708e+15 13667
## - MPG:TrustedYes 1 7.2547e+12 9.3717e+15 13667
## - I(SPG^2) 1 8.9559e+12 9.3734e+15 13667
## - I(BPG^2) 1 1.3121e+13 9.3776e+15 13667
## - TrustedYes:AgressivenessYes 1 1.3275e+13 9.3778e+15 13667
## - MPG:BPG 1 1.6638e+13 9.3811e+15 13667
## - MPG:AgressivenessYes 1 1.7470e+13 9.3820e+15 13667
## - TOPG:SPG 1 1.8126e+13 9.3826e+15 13667
## - I(APG^2) 1 1.9578e+13 9.3841e+15 13667
## - RPG:TrustedYes 1 2.0582e+13 9.3851e+15 13668
## - SPG:TrustedYes 1 2.4923e+13 9.3894e+15 13668
## - SPG:AgressivenessYes 1 2.5822e+13 9.3903e+15 13668
## - APG:TrustedYes 1 2.9161e+13 9.3937e+15 13668
## - BPG:TrustedYes 1 2.9270e+13 9.3938e+15 13668
## - RPG:SPG 1 3.0774e+13 9.3953e+15 13668
## - PPG:TOPG 1 3.6942e+13 9.4014e+15 13668
## - BPG:AgressivenessYes 1 3.8096e+13 9.4026e+15 13668
## - APG:AgressivenessYes 1 4.1643e+13 9.4061e+15 13668
## <none> 9.3645e+15 13668
## - TOPG:BPG 1 4.5347e+13 9.4098e+15 13669
## - BPG:SPG 1 4.6122e+13 9.4106e+15 13669
## - MPG:SPG 1 6.7645e+13 9.4321e+15 13670
## - APG:SPG 1 7.1384e+13 9.4359e+15 13670
## - PPG:SPG 1 9.3356e+13 9.4578e+15 13671
## - PPG:BPG 1 9.3645e+13 9.4581e+15 13671
## - MPG:APG 1 9.8702e+13 9.4632e+15 13671
## - PPG:AgressivenessYes 1 1.0033e+14 9.4648e+15 13671## Warning: In lm.fit(x, y, offset = offset, singular.ok = singular.ok, ...) :
## extra argument 'trControl' will be disregarded##
## Step: AIC=13666.5
## Salary17_18 ~ MPG + PPG + APG + RPG + TOPG + BPG + SPG + TrustedYes +
## AgressivenessYes + I(MPG^2) + I(PPG^2) + I(APG^2) + I(RPG^2) +
## I(TOPG^2) + I(BPG^2) + I(SPG^2) + MPG:PPG + MPG:APG + MPG:TOPG +
## MPG:BPG + MPG:SPG + MPG:TrustedYes + MPG:AgressivenessYes +
## PPG:APG + PPG:RPG + PPG:TOPG + PPG:BPG + PPG:SPG + PPG:TrustedYes +
## PPG:AgressivenessYes + APG:RPG + APG:TOPG + APG:BPG + APG:SPG +
## APG:TrustedYes + APG:AgressivenessYes + RPG:TOPG + RPG:BPG +
## RPG:SPG + RPG:TrustedYes + RPG:AgressivenessYes + TOPG:BPG +
## TOPG:SPG + TOPG:TrustedYes + TOPG:AgressivenessYes + BPG:SPG +
## BPG:TrustedYes + BPG:AgressivenessYes + SPG:TrustedYes +
## SPG:AgressivenessYes + TrustedYes:AgressivenessYes
##
## Df Sum of Sq RSS AIC
## - APG:RPG 1 2.2567e+10 9.3645e+15 13664
## - PPG:TrustedYes 1 1.3614e+11 9.3646e+15 13664
## - MPG:PPG 1 2.5269e+11 9.3648e+15 13664
## - TOPG:TrustedYes 1 2.9711e+11 9.3648e+15 13664
## - PPG:APG 1 3.3164e+11 9.3648e+15 13664
## - RPG:TOPG 1 3.9702e+11 9.3649e+15 13664
## - APG:TOPG 1 4.8127e+11 9.3650e+15 13664
## - APG:BPG 1 1.1431e+12 9.3657e+15 13665
## - I(TOPG^2) 1 1.3426e+12 9.3659e+15 13665
## - I(MPG^2) 1 1.6173e+12 9.3661e+15 13665
## - RPG:AgressivenessYes 1 1.7265e+12 9.3662e+15 13665
## - TOPG:AgressivenessYes 1 2.3886e+12 9.3669e+15 13665
## - MPG:TOPG 1 2.7010e+12 9.3672e+15 13665
## - I(RPG^2) 1 3.0282e+12 9.3675e+15 13665
## - I(PPG^2) 1 3.9830e+12 9.3685e+15 13665
## - RPG:BPG 1 6.3702e+12 9.3709e+15 13665
## - MPG:TrustedYes 1 7.2413e+12 9.3718e+15 13665
## - PPG:RPG 1 7.8801e+12 9.3724e+15 13665
## - I(SPG^2) 1 9.0281e+12 9.3735e+15 13665
## - TrustedYes:AgressivenessYes 1 1.3291e+13 9.3778e+15 13665
## - I(BPG^2) 1 1.3519e+13 9.3780e+15 13665
## - MPG:AgressivenessYes 1 1.7514e+13 9.3820e+15 13665
## - TOPG:SPG 1 1.8183e+13 9.3827e+15 13665
## - I(APG^2) 1 1.9703e+13 9.3842e+15 13665
## - SPG:TrustedYes 1 2.4942e+13 9.3895e+15 13666
## - MPG:BPG 1 2.5267e+13 9.3898e+15 13666
## - SPG:AgressivenessYes 1 2.5818e+13 9.3903e+15 13666
## - APG:TrustedYes 1 2.9200e+13 9.3937e+15 13666
## - RPG:TrustedYes 1 3.1523e+13 9.3960e+15 13666
## - RPG:SPG 1 3.2854e+13 9.3974e+15 13666
## - BPG:TrustedYes 1 3.4066e+13 9.3986e+15 13666
## - PPG:TOPG 1 3.7622e+13 9.4021e+15 13666
## - BPG:AgressivenessYes 1 3.8428e+13 9.4029e+15 13666
## - APG:AgressivenessYes 1 4.1674e+13 9.4062e+15 13666
## <none> 9.3645e+15 13666
## - BPG:SPG 1 5.0061e+13 9.4146e+15 13667
## - TOPG:BPG 1 5.1271e+13 9.4158e+15 13667
## - MPG:SPG 1 6.8224e+13 9.4327e+15 13668
## - APG:SPG 1 7.1388e+13 9.4359e+15 13668
## + MPG:RPG 1 1.5015e+10 9.3645e+15 13668
## - PPG:SPG 1 9.4009e+13 9.4585e+15 13669
## - PPG:AgressivenessYes 1 1.0037e+14 9.4649e+15 13669
## - MPG:APG 1 1.0054e+14 9.4650e+15 13669
## - PPG:BPG 1 1.1130e+14 9.4758e+15 13670## Warning: In lm.fit(x, y, offset = offset, singular.ok = singular.ok, ...) :
## extra argument 'trControl' will be disregarded##
## Step: AIC=13664.5
## Salary17_18 ~ MPG + PPG + APG + RPG + TOPG + BPG + SPG + TrustedYes +
## AgressivenessYes + I(MPG^2) + I(PPG^2) + I(APG^2) + I(RPG^2) +
## I(TOPG^2) + I(BPG^2) + I(SPG^2) + MPG:PPG + MPG:APG + MPG:TOPG +
## MPG:BPG + MPG:SPG + MPG:TrustedYes + MPG:AgressivenessYes +
## PPG:APG + PPG:RPG + PPG:TOPG + PPG:BPG + PPG:SPG + PPG:TrustedYes +
## PPG:AgressivenessYes + APG:TOPG + APG:BPG + APG:SPG + APG:TrustedYes +
## APG:AgressivenessYes + RPG:TOPG + RPG:BPG + RPG:SPG + RPG:TrustedYes +
## RPG:AgressivenessYes + TOPG:BPG + TOPG:SPG + TOPG:TrustedYes +
## TOPG:AgressivenessYes + BPG:SPG + BPG:TrustedYes + BPG:AgressivenessYes +
## SPG:TrustedYes + SPG:AgressivenessYes + TrustedYes:AgressivenessYes
##
## Df Sum of Sq RSS AIC
## - PPG:TrustedYes 1 1.2878e+11 9.3647e+15 13662
## - MPG:PPG 1 2.4265e+11 9.3648e+15 13662
## - TOPG:TrustedYes 1 2.8131e+11 9.3648e+15 13662
## - PPG:APG 1 3.3836e+11 9.3649e+15 13662
## - APG:TOPG 1 4.5875e+11 9.3650e+15 13662
## - RPG:TOPG 1 9.1740e+11 9.3654e+15 13662
## - I(TOPG^2) 1 1.3709e+12 9.3659e+15 13663
## - APG:BPG 1 1.3873e+12 9.3659e+15 13663
## - I(MPG^2) 1 1.5949e+12 9.3661e+15 13663
## - RPG:AgressivenessYes 1 1.7141e+12 9.3662e+15 13663
## - TOPG:AgressivenessYes 1 2.3957e+12 9.3669e+15 13663
## - MPG:TOPG 1 2.6964e+12 9.3672e+15 13663
## - I(PPG^2) 1 3.9687e+12 9.3685e+15 13663
## - I(RPG^2) 1 4.2967e+12 9.3688e+15 13663
## - RPG:BPG 1 6.3632e+12 9.3709e+15 13663
## - MPG:TrustedYes 1 7.2979e+12 9.3718e+15 13663
## - PPG:RPG 1 7.8581e+12 9.3724e+15 13663
## - I(SPG^2) 1 9.0295e+12 9.3736e+15 13663
## - TrustedYes:AgressivenessYes 1 1.3327e+13 9.3779e+15 13663
## - I(BPG^2) 1 1.4235e+13 9.3788e+15 13663
## - MPG:AgressivenessYes 1 1.7586e+13 9.3821e+15 13663
## - TOPG:SPG 1 1.9341e+13 9.3839e+15 13663
## - I(APG^2) 1 2.2048e+13 9.3866e+15 13664
## - SPG:TrustedYes 1 2.5007e+13 9.3895e+15 13664
## - MPG:BPG 1 2.5704e+13 9.3902e+15 13664
## - SPG:AgressivenessYes 1 2.5888e+13 9.3904e+15 13664
## - APG:TrustedYes 1 3.0659e+13 9.3952e+15 13664
## - RPG:TrustedYes 1 3.2392e+13 9.3969e+15 13664
## - BPG:TrustedYes 1 3.4309e+13 9.3988e+15 13664
## - RPG:SPG 1 3.4845e+13 9.3994e+15 13664
## - PPG:TOPG 1 3.7628e+13 9.4022e+15 13664
## - BPG:AgressivenessYes 1 3.8697e+13 9.4032e+15 13664
## - APG:AgressivenessYes 1 4.2121e+13 9.4067e+15 13664
## <none> 9.3645e+15 13664
## - BPG:SPG 1 5.0733e+13 9.4153e+15 13665
## - TOPG:BPG 1 5.9491e+13 9.4240e+15 13665
## - MPG:SPG 1 6.8269e+13 9.4328e+15 13666
## - APG:SPG 1 7.8252e+13 9.4428e+15 13666
## + APG:RPG 1 2.2567e+10 9.3645e+15 13666
## + MPG:RPG 1 9.1775e+09 9.3645e+15 13666
## - PPG:SPG 1 9.4076e+13 9.4586e+15 13667
## - PPG:AgressivenessYes 1 1.0057e+14 9.4651e+15 13667
## - MPG:APG 1 1.0058e+14 9.4651e+15 13667
## - PPG:BPG 1 1.1143e+14 9.4760e+15 13668## Warning: In lm.fit(x, y, offset = offset, singular.ok = singular.ok, ...) :
## extra argument 'trControl' will be disregarded##
## Step: AIC=13662.51
## Salary17_18 ~ MPG + PPG + APG + RPG + TOPG + BPG + SPG + TrustedYes +
## AgressivenessYes + I(MPG^2) + I(PPG^2) + I(APG^2) + I(RPG^2) +
## I(TOPG^2) + I(BPG^2) + I(SPG^2) + MPG:PPG + MPG:APG + MPG:TOPG +
## MPG:BPG + MPG:SPG + MPG:TrustedYes + MPG:AgressivenessYes +
## PPG:APG + PPG:RPG + PPG:TOPG + PPG:BPG + PPG:SPG + PPG:AgressivenessYes +
## APG:TOPG + APG:BPG + APG:SPG + APG:TrustedYes + APG:AgressivenessYes +
## RPG:TOPG + RPG:BPG + RPG:SPG + RPG:TrustedYes + RPG:AgressivenessYes +
## TOPG:BPG + TOPG:SPG + TOPG:TrustedYes + TOPG:AgressivenessYes +
## BPG:SPG + BPG:TrustedYes + BPG:AgressivenessYes + SPG:TrustedYes +
## SPG:AgressivenessYes + TrustedYes:AgressivenessYes
##
## Df Sum of Sq RSS AIC
## - MPG:PPG 1 1.2435e+11 9.3648e+15 13660
## - TOPG:TrustedYes 1 1.9580e+11 9.3649e+15 13660
## - PPG:APG 1 3.5038e+11 9.3650e+15 13660
## - APG:TOPG 1 4.3992e+11 9.3651e+15 13660
## - RPG:TOPG 1 9.4189e+11 9.3656e+15 13661
## - APG:BPG 1 1.3415e+12 9.3660e+15 13661
## - I(TOPG^2) 1 1.4094e+12 9.3661e+15 13661
## - I(MPG^2) 1 1.5049e+12 9.3662e+15 13661
## - RPG:AgressivenessYes 1 1.7919e+12 9.3665e+15 13661
## - TOPG:AgressivenessYes 1 2.3215e+12 9.3670e+15 13661
## - MPG:TOPG 1 3.2150e+12 9.3679e+15 13661
## - I(PPG^2) 1 3.8649e+12 9.3685e+15 13661
## - I(RPG^2) 1 4.4516e+12 9.3691e+15 13661
## - RPG:BPG 1 6.2518e+12 9.3709e+15 13661
## - PPG:RPG 1 7.9969e+12 9.3727e+15 13661
## - I(SPG^2) 1 9.0416e+12 9.3737e+15 13661
## - MPG:TrustedYes 1 1.0344e+13 9.3750e+15 13661
## - TrustedYes:AgressivenessYes 1 1.3525e+13 9.3782e+15 13661
## - I(BPG^2) 1 1.4208e+13 9.3789e+15 13661
## - MPG:AgressivenessYes 1 1.9173e+13 9.3838e+15 13661
## - TOPG:SPG 1 2.0040e+13 9.3847e+15 13662
## - I(APG^2) 1 2.2053e+13 9.3867e+15 13662
## - SPG:TrustedYes 1 2.4879e+13 9.3895e+15 13662
## - SPG:AgressivenessYes 1 2.5855e+13 9.3905e+15 13662
## - MPG:BPG 1 2.6646e+13 9.3913e+15 13662
## - APG:TrustedYes 1 3.2221e+13 9.3969e+15 13662
## - RPG:TrustedYes 1 3.2286e+13 9.3969e+15 13662
## - RPG:SPG 1 3.4717e+13 9.3994e+15 13662
## - BPG:TrustedYes 1 3.4725e+13 9.3994e+15 13662
## - PPG:TOPG 1 3.7500e+13 9.4022e+15 13662
## - BPG:AgressivenessYes 1 3.8787e+13 9.4034e+15 13662
## - APG:AgressivenessYes 1 4.1996e+13 9.4067e+15 13662
## <none> 9.3647e+15 13662
## - BPG:SPG 1 5.0619e+13 9.4153e+15 13663
## - TOPG:BPG 1 6.0215e+13 9.4249e+15 13663
## - MPG:SPG 1 6.8141e+13 9.4328e+15 13664
## - APG:SPG 1 7.8543e+13 9.4432e+15 13664
## + PPG:TrustedYes 1 1.2878e+11 9.3645e+15 13664
## + APG:RPG 1 1.5215e+10 9.3646e+15 13664
## + MPG:RPG 1 7.2262e+09 9.3647e+15 13664
## - PPG:SPG 1 9.4350e+13 9.4590e+15 13665
## - MPG:APG 1 1.0330e+14 9.4680e+15 13665
## - PPG:AgressivenessYes 1 1.1137e+14 9.4760e+15 13666
## - PPG:BPG 1 1.1360e+14 9.4783e+15 13666## Warning: In lm.fit(x, y, offset = offset, singular.ok = singular.ok, ...) :
## extra argument 'trControl' will be disregarded##
## Step: AIC=13660.51
## Salary17_18 ~ MPG + PPG + APG + RPG + TOPG + BPG + SPG + TrustedYes +
## AgressivenessYes + I(MPG^2) + I(PPG^2) + I(APG^2) + I(RPG^2) +
## I(TOPG^2) + I(BPG^2) + I(SPG^2) + MPG:APG + MPG:TOPG + MPG:BPG +
## MPG:SPG + MPG:TrustedYes + MPG:AgressivenessYes + PPG:APG +
## PPG:RPG + PPG:TOPG + PPG:BPG + PPG:SPG + PPG:AgressivenessYes +
## APG:TOPG + APG:BPG + APG:SPG + APG:TrustedYes + APG:AgressivenessYes +
## RPG:TOPG + RPG:BPG + RPG:SPG + RPG:TrustedYes + RPG:AgressivenessYes +
## TOPG:BPG + TOPG:SPG + TOPG:TrustedYes + TOPG:AgressivenessYes +
## BPG:SPG + BPG:TrustedYes + BPG:AgressivenessYes + SPG:TrustedYes +
## SPG:AgressivenessYes + TrustedYes:AgressivenessYes
##
## Df Sum of Sq RSS AIC
## - TOPG:TrustedYes 1 1.8670e+11 9.3650e+15 13658
## - PPG:APG 1 4.1392e+11 9.3652e+15 13658
## - APG:TOPG 1 4.6939e+11 9.3653e+15 13658
## - RPG:TOPG 1 8.4681e+11 9.3656e+15 13659
## - APG:BPG 1 1.2688e+12 9.3661e+15 13659
## - I(TOPG^2) 1 1.3248e+12 9.3661e+15 13659
## - I(MPG^2) 1 1.5064e+12 9.3663e+15 13659
## - RPG:AgressivenessYes 1 1.7445e+12 9.3665e+15 13659
## - TOPG:AgressivenessYes 1 2.5184e+12 9.3673e+15 13659
## - I(RPG^2) 1 4.5352e+12 9.3693e+15 13659
## - MPG:TOPG 1 4.6731e+12 9.3695e+15 13659
## - RPG:BPG 1 6.2332e+12 9.3710e+15 13659
## - I(PPG^2) 1 7.8778e+12 9.3727e+15 13659
## - PPG:RPG 1 8.1343e+12 9.3729e+15 13659
## - I(SPG^2) 1 9.1621e+12 9.3739e+15 13659
## - MPG:TrustedYes 1 1.0221e+13 9.3750e+15 13659
## - TrustedYes:AgressivenessYes 1 1.3492e+13 9.3783e+15 13659
## - I(BPG^2) 1 1.4238e+13 9.3790e+15 13659
## - MPG:AgressivenessYes 1 1.9091e+13 9.3839e+15 13659
## - TOPG:SPG 1 2.1243e+13 9.3860e+15 13660
## - I(APG^2) 1 2.1939e+13 9.3867e+15 13660
## - SPG:TrustedYes 1 2.4757e+13 9.3895e+15 13660
## - SPG:AgressivenessYes 1 2.6134e+13 9.3909e+15 13660
## - MPG:BPG 1 2.7086e+13 9.3919e+15 13660
## - APG:TrustedYes 1 3.2136e+13 9.3969e+15 13660
## - RPG:TrustedYes 1 3.2230e+13 9.3970e+15 13660
## - RPG:SPG 1 3.4637e+13 9.3994e+15 13660
## - BPG:TrustedYes 1 3.4806e+13 9.3996e+15 13660
## - BPG:AgressivenessYes 1 3.9952e+13 9.4047e+15 13660
## - PPG:TOPG 1 4.1601e+13 9.4064e+15 13660
## - APG:AgressivenessYes 1 4.2063e+13 9.4068e+15 13660
## <none> 9.3648e+15 13660
## - BPG:SPG 1 5.0510e+13 9.4153e+15 13661
## - TOPG:BPG 1 6.0183e+13 9.4250e+15 13661
## - MPG:SPG 1 7.2160e+13 9.4369e+15 13662
## - APG:SPG 1 7.8712e+13 9.4435e+15 13662
## + MPG:PPG 1 1.2435e+11 9.3647e+15 13662
## + MPG:RPG 1 2.0650e+10 9.3648e+15 13662
## + APG:RPG 1 1.1672e+10 9.3648e+15 13662
## + PPG:TrustedYes 1 1.0479e+10 9.3648e+15 13662
## - MPG:APG 1 1.0535e+14 9.4701e+15 13664
## - PPG:SPG 1 1.1119e+14 9.4760e+15 13664
## - PPG:BPG 1 1.1430e+14 9.4791e+15 13664
## - PPG:AgressivenessYes 1 1.1640e+14 9.4812e+15 13664## Warning: In lm.fit(x, y, offset = offset, singular.ok = singular.ok, ...) :
## extra argument 'trControl' will be disregarded##
## Step: AIC=13658.52
## Salary17_18 ~ MPG + PPG + APG + RPG + TOPG + BPG + SPG + TrustedYes +
## AgressivenessYes + I(MPG^2) + I(PPG^2) + I(APG^2) + I(RPG^2) +
## I(TOPG^2) + I(BPG^2) + I(SPG^2) + MPG:APG + MPG:TOPG + MPG:BPG +
## MPG:SPG + MPG:TrustedYes + MPG:AgressivenessYes + PPG:APG +
## PPG:RPG + PPG:TOPG + PPG:BPG + PPG:SPG + PPG:AgressivenessYes +
## APG:TOPG + APG:BPG + APG:SPG + APG:TrustedYes + APG:AgressivenessYes +
## RPG:TOPG + RPG:BPG + RPG:SPG + RPG:TrustedYes + RPG:AgressivenessYes +
## TOPG:BPG + TOPG:SPG + TOPG:AgressivenessYes + BPG:SPG + BPG:TrustedYes +
## BPG:AgressivenessYes + SPG:TrustedYes + SPG:AgressivenessYes +
## TrustedYes:AgressivenessYes
##
## Df Sum of Sq RSS AIC
## - APG:TOPG 1 4.8242e+11 9.3655e+15 13656
## - PPG:APG 1 4.9023e+11 9.3655e+15 13656
## - RPG:TOPG 1 9.5968e+11 9.3659e+15 13657
## - APG:BPG 1 1.2931e+12 9.3663e+15 13657
## - I(TOPG^2) 1 1.3005e+12 9.3663e+15 13657
## - I(MPG^2) 1 1.6787e+12 9.3667e+15 13657
## - RPG:AgressivenessYes 1 1.6907e+12 9.3667e+15 13657
## - TOPG:AgressivenessYes 1 2.4158e+12 9.3674e+15 13657
## - I(RPG^2) 1 4.5624e+12 9.3695e+15 13657
## - RPG:BPG 1 6.4570e+12 9.3714e+15 13657
## - I(PPG^2) 1 7.9625e+12 9.3729e+15 13657
## - MPG:TOPG 1 8.0629e+12 9.3730e+15 13657
## - PPG:RPG 1 8.4017e+12 9.3734e+15 13657
## - I(SPG^2) 1 9.0593e+12 9.3740e+15 13657
## - MPG:TrustedYes 1 1.0039e+13 9.3750e+15 13657
## - I(BPG^2) 1 1.5517e+13 9.3805e+15 13657
## - TrustedYes:AgressivenessYes 1 1.7744e+13 9.3827e+15 13657
## - MPG:AgressivenessYes 1 1.9305e+13 9.3843e+15 13657
## - TOPG:SPG 1 2.1930e+13 9.3869e+15 13658
## - I(APG^2) 1 2.2290e+13 9.3873e+15 13658
## - SPG:TrustedYes 1 2.4640e+13 9.3896e+15 13658
## - SPG:AgressivenessYes 1 2.6352e+13 9.3913e+15 13658
## - MPG:BPG 1 2.9989e+13 9.3950e+15 13658
## - RPG:TrustedYes 1 3.3102e+13 9.3981e+15 13658
## - RPG:SPG 1 3.4844e+13 9.3998e+15 13658
## - BPG:TrustedYes 1 3.6029e+13 9.4010e+15 13658
## - BPG:AgressivenessYes 1 3.9777e+13 9.4047e+15 13658
## - PPG:TOPG 1 4.1778e+13 9.4067e+15 13658
## - APG:AgressivenessYes 1 4.2261e+13 9.4072e+15 13658
## <none> 9.3650e+15 13658
## - APG:TrustedYes 1 4.4841e+13 9.4098e+15 13659
## - BPG:SPG 1 5.1080e+13 9.4161e+15 13659
## - TOPG:BPG 1 6.0620e+13 9.4256e+15 13659
## - MPG:SPG 1 7.1973e+13 9.4369e+15 13660
## - APG:SPG 1 8.0356e+13 9.4453e+15 13660
## + TOPG:TrustedYes 1 1.8670e+11 9.3648e+15 13660
## + MPG:PPG 1 1.1525e+11 9.3649e+15 13660
## + MPG:RPG 1 2.6494e+10 9.3649e+15 13660
## + APG:RPG 1 3.7239e+09 9.3650e+15 13660
## + PPG:TrustedYes 1 1.9928e+07 9.3650e+15 13660
## - PPG:SPG 1 1.1100e+14 9.4760e+15 13662
## - MPG:APG 1 1.1454e+14 9.4795e+15 13662
## - PPG:AgressivenessYes 1 1.1648e+14 9.4815e+15 13662
## - PPG:BPG 1 1.1727e+14 9.4822e+15 13662## Warning: In lm.fit(x, y, offset = offset, singular.ok = singular.ok, ...) :
## extra argument 'trControl' will be disregarded##
## Step: AIC=13656.55
## Salary17_18 ~ MPG + PPG + APG + RPG + TOPG + BPG + SPG + TrustedYes +
## AgressivenessYes + I(MPG^2) + I(PPG^2) + I(APG^2) + I(RPG^2) +
## I(TOPG^2) + I(BPG^2) + I(SPG^2) + MPG:APG + MPG:TOPG + MPG:BPG +
## MPG:SPG + MPG:TrustedYes + MPG:AgressivenessYes + PPG:APG +
## PPG:RPG + PPG:TOPG + PPG:BPG + PPG:SPG + PPG:AgressivenessYes +
## APG:BPG + APG:SPG + APG:TrustedYes + APG:AgressivenessYes +
## RPG:TOPG + RPG:BPG + RPG:SPG + RPG:TrustedYes + RPG:AgressivenessYes +
## TOPG:BPG + TOPG:SPG + TOPG:AgressivenessYes + BPG:SPG + BPG:TrustedYes +
## BPG:AgressivenessYes + SPG:TrustedYes + SPG:AgressivenessYes +
## TrustedYes:AgressivenessYes
##
## Df Sum of Sq RSS AIC
## - PPG:APG 1 1.9708e+11 9.3657e+15 13655
## - RPG:TOPG 1 1.0724e+12 9.3665e+15 13655
## - I(MPG^2) 1 1.5912e+12 9.3670e+15 13655
## - RPG:AgressivenessYes 1 1.6351e+12 9.3671e+15 13655
## - APG:BPG 1 1.6764e+12 9.3671e+15 13655
## - TOPG:AgressivenessYes 1 1.9814e+12 9.3674e+15 13655
## - I(RPG^2) 1 4.3696e+12 9.3698e+15 13655
## - RPG:BPG 1 6.7727e+12 9.3722e+15 13655
## - MPG:TOPG 1 7.7339e+12 9.3732e+15 13655
## - I(TOPG^2) 1 8.2905e+12 9.3737e+15 13655
## - I(SPG^2) 1 8.6874e+12 9.3741e+15 13655
## - PPG:RPG 1 8.8313e+12 9.3743e+15 13655
## - I(PPG^2) 1 8.9927e+12 9.3744e+15 13655
## - MPG:TrustedYes 1 1.0194e+13 9.3756e+15 13655
## - I(BPG^2) 1 1.6560e+13 9.3820e+15 13655
## - TrustedYes:AgressivenessYes 1 1.8171e+13 9.3836e+15 13655
## - MPG:AgressivenessYes 1 1.9739e+13 9.3852e+15 13656
## - TOPG:SPG 1 2.5352e+13 9.3908e+15 13656
## - SPG:TrustedYes 1 2.5554e+13 9.3910e+15 13656
## - SPG:AgressivenessYes 1 2.7871e+13 9.3933e+15 13656
## - MPG:BPG 1 3.2261e+13 9.3977e+15 13656
## - RPG:TrustedYes 1 3.3311e+13 9.3988e+15 13656
## - RPG:SPG 1 3.4730e+13 9.4002e+15 13656
## - BPG:TrustedYes 1 3.5548e+13 9.4010e+15 13656
## - BPG:AgressivenessYes 1 3.9295e+13 9.4047e+15 13656
## - I(APG^2) 1 3.9996e+13 9.4054e+15 13656
## <none> 9.3655e+15 13656
## - APG:AgressivenessYes 1 4.3223e+13 9.4087e+15 13657
## - APG:TrustedYes 1 4.6768e+13 9.4122e+15 13657
## - BPG:SPG 1 5.0618e+13 9.4161e+15 13657
## - PPG:TOPG 1 5.2181e+13 9.4176e+15 13657
## - TOPG:BPG 1 6.9170e+13 9.4346e+15 13658
## - MPG:SPG 1 7.2512e+13 9.4380e+15 13658
## - APG:SPG 1 8.0613e+13 9.4461e+15 13658
## + APG:TOPG 1 4.8242e+11 9.3650e+15 13658
## + TOPG:TrustedYes 1 1.9973e+11 9.3653e+15 13658
## + MPG:PPG 1 1.4378e+11 9.3653e+15 13658
## + MPG:RPG 1 2.5564e+10 9.3654e+15 13658
## + APG:RPG 1 7.0298e+09 9.3654e+15 13658
## + PPG:TrustedYes 1 2.7875e+09 9.3655e+15 13658
## - PPG:SPG 1 1.1130e+14 9.4768e+15 13660
## - MPG:APG 1 1.1521e+14 9.4807e+15 13660
## - PPG:BPG 1 1.1679e+14 9.4822e+15 13660
## - PPG:AgressivenessYes 1 1.1804e+14 9.4835e+15 13660## Warning: In lm.fit(x, y, offset = offset, singular.ok = singular.ok, ...) :
## extra argument 'trControl' will be disregarded##
## Step: AIC=13654.56
## Salary17_18 ~ MPG + PPG + APG + RPG + TOPG + BPG + SPG + TrustedYes +
## AgressivenessYes + I(MPG^2) + I(PPG^2) + I(APG^2) + I(RPG^2) +
## I(TOPG^2) + I(BPG^2) + I(SPG^2) + MPG:APG + MPG:TOPG + MPG:BPG +
## MPG:SPG + MPG:TrustedYes + MPG:AgressivenessYes + PPG:RPG +
## PPG:TOPG + PPG:BPG + PPG:SPG + PPG:AgressivenessYes + APG:BPG +
## APG:SPG + APG:TrustedYes + APG:AgressivenessYes + RPG:TOPG +
## RPG:BPG + RPG:SPG + RPG:TrustedYes + RPG:AgressivenessYes +
## TOPG:BPG + TOPG:SPG + TOPG:AgressivenessYes + BPG:SPG + BPG:TrustedYes +
## BPG:AgressivenessYes + SPG:TrustedYes + SPG:AgressivenessYes +
## TrustedYes:AgressivenessYes
##
## Df Sum of Sq RSS AIC
## - RPG:TOPG 1 1.1092e+12 9.3668e+15 13653
## - APG:BPG 1 1.5482e+12 9.3672e+15 13653
## - RPG:AgressivenessYes 1 1.6194e+12 9.3673e+15 13653
## - I(MPG^2) 1 1.6196e+12 9.3673e+15 13653
## - TOPG:AgressivenessYes 1 2.0186e+12 9.3677e+15 13653
## - I(RPG^2) 1 4.2385e+12 9.3699e+15 13653
## - RPG:BPG 1 6.9016e+12 9.3726e+15 13653
## - MPG:TOPG 1 8.1566e+12 9.3738e+15 13653
## - I(SPG^2) 1 8.4942e+12 9.3741e+15 13653
## - I(TOPG^2) 1 8.7083e+12 9.3744e+15 13653
## - I(PPG^2) 1 9.2592e+12 9.3749e+15 13653
## - PPG:RPG 1 9.6370e+12 9.3753e+15 13653
## - MPG:TrustedYes 1 1.0161e+13 9.3758e+15 13653
## - I(BPG^2) 1 1.6504e+13 9.3822e+15 13653
## - TrustedYes:AgressivenessYes 1 1.7980e+13 9.3836e+15 13653
## - MPG:AgressivenessYes 1 1.9591e+13 9.3852e+15 13654
## - SPG:TrustedYes 1 2.5368e+13 9.3910e+15 13654
## - TOPG:SPG 1 2.5392e+13 9.3910e+15 13654
## - SPG:AgressivenessYes 1 2.8179e+13 9.3938e+15 13654
## - RPG:TrustedYes 1 3.4016e+13 9.3997e+15 13654
## - MPG:BPG 1 3.4151e+13 9.3998e+15 13654
## - RPG:SPG 1 3.5261e+13 9.4009e+15 13654
## - BPG:TrustedYes 1 3.7744e+13 9.4034e+15 13654
## - BPG:AgressivenessYes 1 4.0092e+13 9.4057e+15 13654
## - I(APG^2) 1 4.1116e+13 9.4068e+15 13654
## <none> 9.3657e+15 13655
## - APG:AgressivenessYes 1 4.3279e+13 9.4089e+15 13655
## - APG:TrustedYes 1 4.8112e+13 9.4138e+15 13655
## - BPG:SPG 1 5.0534e+13 9.4162e+15 13655
## - TOPG:BPG 1 7.1206e+13 9.4369e+15 13656
## - MPG:SPG 1 7.3843e+13 9.4395e+15 13656
## - PPG:TOPG 1 7.9325e+13 9.4450e+15 13656
## + TOPG:TrustedYes 1 2.4793e+11 9.3654e+15 13656
## + PPG:APG 1 1.9708e+11 9.3655e+15 13656
## + APG:TOPG 1 1.8926e+11 9.3655e+15 13656
## + MPG:PPG 1 1.8259e+11 9.3655e+15 13656
## + MPG:RPG 1 1.3299e+10 9.3656e+15 13657
## + PPG:TrustedYes 1 5.7733e+09 9.3656e+15 13657
## + APG:RPG 1 1.0364e+09 9.3656e+15 13657
## - APG:SPG 1 8.6783e+13 9.4524e+15 13657
## - PPG:AgressivenessYes 1 1.1835e+14 9.4840e+15 13658
## - PPG:BPG 1 1.2137e+14 9.4870e+15 13658
## - PPG:SPG 1 1.3151e+14 9.4972e+15 13659
## - MPG:APG 1 1.9011e+14 9.5558e+15 13661## Warning: In lm.fit(x, y, offset = offset, singular.ok = singular.ok, ...) :
## extra argument 'trControl' will be disregarded##
## Step: AIC=13652.61
## Salary17_18 ~ MPG + PPG + APG + RPG + TOPG + BPG + SPG + TrustedYes +
## AgressivenessYes + I(MPG^2) + I(PPG^2) + I(APG^2) + I(RPG^2) +
## I(TOPG^2) + I(BPG^2) + I(SPG^2) + MPG:APG + MPG:TOPG + MPG:BPG +
## MPG:SPG + MPG:TrustedYes + MPG:AgressivenessYes + PPG:RPG +
## PPG:TOPG + PPG:BPG + PPG:SPG + PPG:AgressivenessYes + APG:BPG +
## APG:SPG + APG:TrustedYes + APG:AgressivenessYes + RPG:BPG +
## RPG:SPG + RPG:TrustedYes + RPG:AgressivenessYes + TOPG:BPG +
## TOPG:SPG + TOPG:AgressivenessYes + BPG:SPG + BPG:TrustedYes +
## BPG:AgressivenessYes + SPG:TrustedYes + SPG:AgressivenessYes +
## TrustedYes:AgressivenessYes
##
## Df Sum of Sq RSS AIC
## - APG:BPG 1 1.4991e+12 9.3683e+15 13651
## - I(MPG^2) 1 1.7599e+12 9.3685e+15 13651
## - TOPG:AgressivenessYes 1 2.2854e+12 9.3690e+15 13651
## - RPG:AgressivenessYes 1 3.6081e+12 9.3704e+15 13651
## - I(RPG^2) 1 4.3847e+12 9.3711e+15 13651
## - RPG:BPG 1 6.7756e+12 9.3735e+15 13651
## - I(TOPG^2) 1 7.7670e+12 9.3745e+15 13651
## - MPG:TOPG 1 8.5949e+12 9.3754e+15 13651
## - I(SPG^2) 1 9.0159e+12 9.3758e+15 13651
## - I(PPG^2) 1 9.3269e+12 9.3761e+15 13651
## - PPG:RPG 1 1.0279e+13 9.3770e+15 13651
## - MPG:TrustedYes 1 1.0375e+13 9.3771e+15 13651
## - I(BPG^2) 1 1.6113e+13 9.3829e+15 13651
## - TrustedYes:AgressivenessYes 1 1.7947e+13 9.3847e+15 13652
## - MPG:AgressivenessYes 1 1.9871e+13 9.3866e+15 13652
## - SPG:TrustedYes 1 2.5403e+13 9.3922e+15 13652
## - TOPG:SPG 1 2.6124e+13 9.3929e+15 13652
## - SPG:AgressivenessYes 1 2.8370e+13 9.3951e+15 13652
## - RPG:TrustedYes 1 3.2907e+13 9.3997e+15 13652
## - MPG:BPG 1 3.3156e+13 9.3999e+15 13652
## - RPG:SPG 1 3.6104e+13 9.4029e+15 13652
## - BPG:TrustedYes 1 3.7100e+13 9.4039e+15 13652
## - BPG:AgressivenessYes 1 3.8983e+13 9.4057e+15 13652
## <none> 9.3668e+15 13653
## - I(APG^2) 1 4.3453e+13 9.4102e+15 13653
## - APG:AgressivenessYes 1 4.4710e+13 9.4115e+15 13653
## - APG:TrustedYes 1 4.8817e+13 9.4156e+15 13653
## - BPG:SPG 1 4.9674e+13 9.4164e+15 13653
## - MPG:SPG 1 7.3347e+13 9.4401e+15 13654
## - TOPG:BPG 1 8.1227e+13 9.4480e+15 13654
## - PPG:TOPG 1 8.1691e+13 9.4485e+15 13654
## + RPG:TOPG 1 1.1092e+12 9.3657e+15 13655
## + APG:RPG 1 4.2003e+11 9.3663e+15 13655
## + TOPG:TrustedYes 1 3.9335e+11 9.3664e+15 13655
## + APG:TOPG 1 2.3990e+11 9.3665e+15 13655
## + PPG:APG 1 2.3385e+11 9.3665e+15 13655
## + MPG:RPG 1 9.1131e+10 9.3667e+15 13655
## + MPG:PPG 1 5.0223e+10 9.3667e+15 13655
## + PPG:TrustedYes 1 6.6670e+08 9.3668e+15 13655
## - APG:SPG 1 9.0318e+13 9.4571e+15 13655
## - PPG:AgressivenessYes 1 1.2444e+14 9.4912e+15 13656
## - PPG:SPG 1 1.3341e+14 9.5002e+15 13657
## - PPG:BPG 1 1.3484e+14 9.5016e+15 13657
## - MPG:APG 1 1.9187e+14 9.5586e+15 13660## Warning: In lm.fit(x, y, offset = offset, singular.ok = singular.ok, ...) :
## extra argument 'trControl' will be disregarded##
## Step: AIC=13650.68
## Salary17_18 ~ MPG + PPG + APG + RPG + TOPG + BPG + SPG + TrustedYes +
## AgressivenessYes + I(MPG^2) + I(PPG^2) + I(APG^2) + I(RPG^2) +
## I(TOPG^2) + I(BPG^2) + I(SPG^2) + MPG:APG + MPG:TOPG + MPG:BPG +
## MPG:SPG + MPG:TrustedYes + MPG:AgressivenessYes + PPG:RPG +
## PPG:TOPG + PPG:BPG + PPG:SPG + PPG:AgressivenessYes + APG:SPG +
## APG:TrustedYes + APG:AgressivenessYes + RPG:BPG + RPG:SPG +
## RPG:TrustedYes + RPG:AgressivenessYes + TOPG:BPG + TOPG:SPG +
## TOPG:AgressivenessYes + BPG:SPG + BPG:TrustedYes + BPG:AgressivenessYes +
## SPG:TrustedYes + SPG:AgressivenessYes + TrustedYes:AgressivenessYes
##
## Df Sum of Sq RSS AIC
## - I(MPG^2) 1 1.5141e+12 9.3698e+15 13649
## - TOPG:AgressivenessYes 1 1.7904e+12 9.3700e+15 13649
## - RPG:AgressivenessYes 1 3.4474e+12 9.3717e+15 13649
## - I(RPG^2) 1 4.0577e+12 9.3723e+15 13649
## - RPG:BPG 1 6.2239e+12 9.3745e+15 13649
## - MPG:TOPG 1 8.8921e+12 9.3772e+15 13649
## - I(SPG^2) 1 9.6523e+12 9.3779e+15 13649
## - I(PPG^2) 1 9.7113e+12 9.3780e+15 13649
## - PPG:RPG 1 9.9740e+12 9.3782e+15 13649
## - I(TOPG^2) 1 1.0346e+13 9.3786e+15 13649
## - MPG:TrustedYes 1 1.0810e+13 9.3791e+15 13649
## - TrustedYes:AgressivenessYes 1 1.9199e+13 9.3875e+15 13650
## - MPG:AgressivenessYes 1 2.1070e+13 9.3893e+15 13650
## - I(BPG^2) 1 2.1302e+13 9.3896e+15 13650
## - SPG:TrustedYes 1 2.6679e+13 9.3949e+15 13650
## - TOPG:SPG 1 2.8869e+13 9.3971e+15 13650
## - SPG:AgressivenessYes 1 3.0909e+13 9.3992e+15 13650
## - RPG:TrustedYes 1 3.1770e+13 9.4000e+15 13650
## - BPG:TrustedYes 1 3.5602e+13 9.4039e+15 13650
## - RPG:SPG 1 3.6403e+13 9.4047e+15 13650
## - BPG:AgressivenessYes 1 3.7899e+13 9.4062e+15 13650
## - MPG:BPG 1 4.1339e+13 9.4096e+15 13651
## <none> 9.3683e+15 13651
## - APG:AgressivenessYes 1 4.3336e+13 9.4116e+15 13651
## - I(APG^2) 1 4.8333e+13 9.4166e+15 13651
## - BPG:SPG 1 4.8857e+13 9.4171e+15 13651
## - APG:TrustedYes 1 5.3774e+13 9.4220e+15 13651
## - MPG:SPG 1 7.8377e+13 9.4466e+15 13652
## + APG:BPG 1 1.4991e+12 9.3668e+15 13653
## + RPG:TOPG 1 1.0601e+12 9.3672e+15 13653
## + APG:TOPG 1 5.7929e+11 9.3677e+15 13653
## + TOPG:TrustedYes 1 4.0676e+11 9.3679e+15 13653
## + PPG:APG 1 9.2338e+10 9.3682e+15 13653
## + MPG:RPG 1 8.9598e+10 9.3682e+15 13653
## + MPG:PPG 1 7.3764e+09 9.3683e+15 13653
## + APG:RPG 1 5.5695e+08 9.3683e+15 13653
## + PPG:TrustedYes 1 4.5983e+08 9.3683e+15 13653
## - PPG:TOPG 1 8.6653e+13 9.4549e+15 13653
## - APG:SPG 1 8.8853e+13 9.4571e+15 13653
## - TOPG:BPG 1 9.8147e+13 9.4664e+15 13653
## - PPG:AgressivenessYes 1 1.2851e+14 9.4968e+15 13655
## - PPG:SPG 1 1.3195e+14 9.5002e+15 13655
## - PPG:BPG 1 1.3506e+14 9.5033e+15 13655
## - MPG:APG 1 2.4834e+14 9.6166e+15 13660## Warning: In lm.fit(x, y, offset = offset, singular.ok = singular.ok, ...) :
## extra argument 'trControl' will be disregarded##
## Step: AIC=13648.75
## Salary17_18 ~ MPG + PPG + APG + RPG + TOPG + BPG + SPG + TrustedYes +
## AgressivenessYes + I(PPG^2) + I(APG^2) + I(RPG^2) + I(TOPG^2) +
## I(BPG^2) + I(SPG^2) + MPG:APG + MPG:TOPG + MPG:BPG + MPG:SPG +
## MPG:TrustedYes + MPG:AgressivenessYes + PPG:RPG + PPG:TOPG +
## PPG:BPG + PPG:SPG + PPG:AgressivenessYes + APG:SPG + APG:TrustedYes +
## APG:AgressivenessYes + RPG:BPG + RPG:SPG + RPG:TrustedYes +
## RPG:AgressivenessYes + TOPG:BPG + TOPG:SPG + TOPG:AgressivenessYes +
## BPG:SPG + BPG:TrustedYes + BPG:AgressivenessYes + SPG:TrustedYes +
## SPG:AgressivenessYes + TrustedYes:AgressivenessYes
##
## Df Sum of Sq RSS AIC
## - TOPG:AgressivenessYes 1 1.3533e+12 9.3711e+15 13647
## - RPG:AgressivenessYes 1 3.6304e+12 9.3734e+15 13647
## - I(RPG^2) 1 3.8098e+12 9.3736e+15 13647
## - RPG:BPG 1 6.3122e+12 9.3761e+15 13647
## - MPG:TOPG 1 7.4372e+12 9.3772e+15 13647
## - I(SPG^2) 1 8.6212e+12 9.3784e+15 13647
## - PPG:RPG 1 1.0768e+13 9.3805e+15 13647
## - I(TOPG^2) 1 1.1215e+13 9.3810e+15 13647
## - I(PPG^2) 1 1.3031e+13 9.3828e+15 13647
## - TrustedYes:AgressivenessYes 1 1.8430e+13 9.3882e+15 13648
## - I(BPG^2) 1 2.1020e+13 9.3908e+15 13648
## - MPG:AgressivenessYes 1 2.1320e+13 9.3911e+15 13648
## - SPG:TrustedYes 1 2.5341e+13 9.3951e+15 13648
## - TOPG:SPG 1 2.7912e+13 9.3977e+15 13648
## - SPG:AgressivenessYes 1 3.1907e+13 9.4017e+15 13648
## - RPG:TrustedYes 1 3.2099e+13 9.4019e+15 13648
## - BPG:TrustedYes 1 3.4698e+13 9.4045e+15 13648
## - RPG:SPG 1 3.7390e+13 9.4072e+15 13648
## - BPG:AgressivenessYes 1 3.7793e+13 9.4076e+15 13648
## <none> 9.3698e+15 13649
## - MPG:TrustedYes 1 4.2526e+13 9.4123e+15 13649
## - APG:AgressivenessYes 1 4.3139e+13 9.4129e+15 13649
## - MPG:BPG 1 4.4722e+13 9.4145e+15 13649
## - I(APG^2) 1 4.8087e+13 9.4179e+15 13649
## - BPG:SPG 1 5.2863e+13 9.4226e+15 13649
## - APG:TrustedYes 1 5.4718e+13 9.4245e+15 13649
## + I(MPG^2) 1 1.5141e+12 9.3683e+15 13651
## + APG:BPG 1 1.2534e+12 9.3685e+15 13651
## + RPG:TOPG 1 1.1914e+12 9.3686e+15 13651
## + TOPG:TrustedYes 1 6.4223e+11 9.3691e+15 13651
## + MPG:RPG 1 4.7163e+11 9.3693e+15 13651
## + APG:TOPG 1 4.4924e+11 9.3693e+15 13651
## + MPG:PPG 1 3.3284e+11 9.3694e+15 13651
## - MPG:SPG 1 8.4875e+13 9.4546e+15 13651
## + PPG:APG 1 1.2261e+11 9.3697e+15 13651
## + PPG:TrustedYes 1 2.0228e+10 9.3698e+15 13651
## + APG:RPG 1 1.8100e+05 9.3698e+15 13651
## - APG:SPG 1 8.8782e+13 9.4586e+15 13651
## - PPG:TOPG 1 9.6768e+13 9.4665e+15 13651
## - TOPG:BPG 1 1.0529e+14 9.4751e+15 13652
## - PPG:AgressivenessYes 1 1.3019e+14 9.5000e+15 13653
## - PPG:SPG 1 1.3053e+14 9.5003e+15 13653
## - PPG:BPG 1 1.4509e+14 9.5149e+15 13654
## - MPG:APG 1 2.4990e+14 9.6197e+15 13658## Warning: In lm.fit(x, y, offset = offset, singular.ok = singular.ok, ...) :
## extra argument 'trControl' will be disregarded##
## Step: AIC=13646.81
## Salary17_18 ~ MPG + PPG + APG + RPG + TOPG + BPG + SPG + TrustedYes +
## AgressivenessYes + I(PPG^2) + I(APG^2) + I(RPG^2) + I(TOPG^2) +
## I(BPG^2) + I(SPG^2) + MPG:APG + MPG:TOPG + MPG:BPG + MPG:SPG +
## MPG:TrustedYes + MPG:AgressivenessYes + PPG:RPG + PPG:TOPG +
## PPG:BPG + PPG:SPG + PPG:AgressivenessYes + APG:SPG + APG:TrustedYes +
## APG:AgressivenessYes + RPG:BPG + RPG:SPG + RPG:TrustedYes +
## RPG:AgressivenessYes + TOPG:BPG + TOPG:SPG + BPG:SPG + BPG:TrustedYes +
## BPG:AgressivenessYes + SPG:TrustedYes + SPG:AgressivenessYes +
## TrustedYes:AgressivenessYes
##
## Df Sum of Sq RSS AIC
## - RPG:AgressivenessYes 1 3.4497e+12 9.3746e+15 13645
## - I(RPG^2) 1 4.2658e+12 9.3754e+15 13645
## - RPG:BPG 1 5.9588e+12 9.3771e+15 13645
## - MPG:TOPG 1 6.2668e+12 9.3774e+15 13645
## - I(SPG^2) 1 9.3737e+12 9.3805e+15 13645
## - PPG:RPG 1 9.8940e+12 9.3810e+15 13645
## - I(PPG^2) 1 1.2960e+13 9.3841e+15 13645
## - TrustedYes:AgressivenessYes 1 1.8938e+13 9.3901e+15 13646
## - I(TOPG^2) 1 1.9499e+13 9.3906e+15 13646
## - I(BPG^2) 1 2.0131e+13 9.3913e+15 13646
## - TOPG:SPG 1 2.6746e+13 9.3979e+15 13646
## - SPG:TrustedYes 1 2.6788e+13 9.3979e+15 13646
## - MPG:AgressivenessYes 1 2.9446e+13 9.4006e+15 13646
## - SPG:AgressivenessYes 1 3.1236e+13 9.4024e+15 13646
## - RPG:TrustedYes 1 3.1269e+13 9.4024e+15 13646
## - BPG:TrustedYes 1 3.4456e+13 9.4056e+15 13646
## - BPG:AgressivenessYes 1 3.6440e+13 9.4076e+15 13646
## - RPG:SPG 1 3.7601e+13 9.4087e+15 13647
## <none> 9.3711e+15 13647
## - MPG:BPG 1 4.3380e+13 9.4145e+15 13647
## - MPG:TrustedYes 1 4.3466e+13 9.4146e+15 13647
## - APG:AgressivenessYes 1 4.6460e+13 9.4176e+15 13647
## - I(APG^2) 1 4.7619e+13 9.4187e+15 13647
## - BPG:SPG 1 5.2092e+13 9.4232e+15 13647
## - APG:TrustedYes 1 5.3704e+13 9.4248e+15 13647
## + RPG:TOPG 1 1.3913e+12 9.3697e+15 13649
## + TOPG:AgressivenessYes 1 1.3533e+12 9.3698e+15 13649
## + I(MPG^2) 1 1.0770e+12 9.3700e+15 13649
## + APG:BPG 1 8.8401e+11 9.3702e+15 13649
## + MPG:RPG 1 4.2754e+11 9.3707e+15 13649
## + PPG:APG 1 1.6515e+11 9.3710e+15 13649
## + MPG:PPG 1 9.8102e+10 9.3710e+15 13649
## + APG:TOPG 1 7.4171e+10 9.3711e+15 13649
## + APG:RPG 1 6.1227e+10 9.3711e+15 13649
## + TOPG:TrustedYes 1 2.7378e+10 9.3711e+15 13649
## + PPG:TrustedYes 1 1.7689e+10 9.3711e+15 13649
## - APG:SPG 1 8.7457e+13 9.4586e+15 13649
## - MPG:SPG 1 8.8666e+13 9.4598e+15 13649
## - TOPG:BPG 1 1.0504e+14 9.4762e+15 13650
## - PPG:TOPG 1 1.1293e+14 9.4841e+15 13650
## - PPG:SPG 1 1.3310e+14 9.5042e+15 13651
## - PPG:BPG 1 1.4374e+14 9.5149e+15 13652
## - PPG:AgressivenessYes 1 1.7402e+14 9.5451e+15 13653
## - MPG:APG 1 2.5383e+14 9.6250e+15 13657## Warning: In lm.fit(x, y, offset = offset, singular.ok = singular.ok, ...) :
## extra argument 'trControl' will be disregarded##
## Step: AIC=13644.98
## Salary17_18 ~ MPG + PPG + APG + RPG + TOPG + BPG + SPG + TrustedYes +
## AgressivenessYes + I(PPG^2) + I(APG^2) + I(RPG^2) + I(TOPG^2) +
## I(BPG^2) + I(SPG^2) + MPG:APG + MPG:TOPG + MPG:BPG + MPG:SPG +
## MPG:TrustedYes + MPG:AgressivenessYes + PPG:RPG + PPG:TOPG +
## PPG:BPG + PPG:SPG + PPG:AgressivenessYes + APG:SPG + APG:TrustedYes +
## APG:AgressivenessYes + RPG:BPG + RPG:SPG + RPG:TrustedYes +
## TOPG:BPG + TOPG:SPG + BPG:SPG + BPG:TrustedYes + BPG:AgressivenessYes +
## SPG:TrustedYes + SPG:AgressivenessYes + TrustedYes:AgressivenessYes
##
## Df Sum of Sq RSS AIC
## - I(RPG^2) 1 2.6680e+12 9.3772e+15 13643
## - MPG:TOPG 1 7.4564e+12 9.3820e+15 13643
## - RPG:BPG 1 7.9417e+12 9.3825e+15 13643
## - PPG:RPG 1 7.9681e+12 9.3825e+15 13643
## - I(SPG^2) 1 9.8488e+12 9.3844e+15 13643
## - I(PPG^2) 1 1.3526e+13 9.3881e+15 13644
## - TrustedYes:AgressivenessYes 1 1.9321e+13 9.3939e+15 13644
## - I(TOPG^2) 1 1.9429e+13 9.3940e+15 13644
## - I(BPG^2) 1 2.2191e+13 9.3968e+15 13644
## - SPG:TrustedYes 1 2.6436e+13 9.4010e+15 13644
## - TOPG:SPG 1 2.7370e+13 9.4019e+15 13644
## - SPG:AgressivenessYes 1 3.2144e+13 9.4067e+15 13644
## - MPG:AgressivenessYes 1 3.3631e+13 9.4082e+15 13645
## - RPG:SPG 1 3.6862e+13 9.4114e+15 13645
## - BPG:TrustedYes 1 4.0573e+13 9.4151e+15 13645
## <none> 9.3746e+15 13645
## - APG:AgressivenessYes 1 4.3411e+13 9.4180e+15 13645
## - MPG:BPG 1 4.4999e+13 9.4196e+15 13645
## - RPG:TrustedYes 1 4.6602e+13 9.4212e+15 13645
## - I(APG^2) 1 4.6857e+13 9.4214e+15 13645
## - MPG:TrustedYes 1 5.1721e+13 9.4263e+15 13645
## - BPG:SPG 1 5.3605e+13 9.4282e+15 13646
## - APG:TrustedYes 1 5.4772e+13 9.4293e+15 13646
## + RPG:AgressivenessYes 1 3.4497e+12 9.3711e+15 13647
## + RPG:TOPG 1 3.4404e+12 9.3711e+15 13647
## - BPG:AgressivenessYes 1 8.2293e+13 9.4569e+15 13647
## + I(MPG^2) 1 1.2531e+12 9.3733e+15 13647
## + TOPG:AgressivenessYes 1 1.1725e+12 9.3734e+15 13647
## + APG:BPG 1 7.7346e+11 9.3738e+15 13647
## + MPG:RPG 1 5.5748e+11 9.3740e+15 13647
## + APG:RPG 1 4.6423e+11 9.3741e+15 13647
## + MPG:PPG 1 3.4212e+11 9.3742e+15 13647
## + PPG:APG 1 1.7539e+11 9.3744e+15 13647
## + APG:TOPG 1 7.6574e+10 9.3745e+15 13647
## + TOPG:TrustedYes 1 4.4791e+10 9.3745e+15 13647
## + PPG:TrustedYes 1 2.2501e+10 9.3746e+15 13647
## - MPG:SPG 1 8.7412e+13 9.4620e+15 13647
## - APG:SPG 1 8.8936e+13 9.4635e+15 13647
## - TOPG:BPG 1 1.0595e+14 9.4805e+15 13648
## - PPG:TOPG 1 1.1076e+14 9.4853e+15 13648
## - PPG:SPG 1 1.3146e+14 9.5060e+15 13649
## - PPG:BPG 1 1.4037e+14 9.5149e+15 13650
## - PPG:AgressivenessYes 1 1.7082e+14 9.5454e+15 13651
## - MPG:APG 1 2.5329e+14 9.6279e+15 13655## Warning: In lm.fit(x, y, offset = offset, singular.ok = singular.ok, ...) :
## extra argument 'trControl' will be disregarded##
## Step: AIC=13643.1
## Salary17_18 ~ MPG + PPG + APG + RPG + TOPG + BPG + SPG + TrustedYes +
## AgressivenessYes + I(PPG^2) + I(APG^2) + I(TOPG^2) + I(BPG^2) +
## I(SPG^2) + MPG:APG + MPG:TOPG + MPG:BPG + MPG:SPG + MPG:TrustedYes +
## MPG:AgressivenessYes + PPG:RPG + PPG:TOPG + PPG:BPG + PPG:SPG +
## PPG:AgressivenessYes + APG:SPG + APG:TrustedYes + APG:AgressivenessYes +
## RPG:BPG + RPG:SPG + RPG:TrustedYes + TOPG:BPG + TOPG:SPG +
## BPG:SPG + BPG:TrustedYes + BPG:AgressivenessYes + SPG:TrustedYes +
## SPG:AgressivenessYes + TrustedYes:AgressivenessYes
##
## Df Sum of Sq RSS AIC
## - MPG:TOPG 1 7.4697e+12 9.3847e+15 13642
## - I(SPG^2) 1 9.5675e+12 9.3868e+15 13642
## - PPG:RPG 1 9.7569e+12 9.3870e+15 13642
## - I(PPG^2) 1 1.2521e+13 9.3898e+15 13642
## - I(TOPG^2) 1 1.8271e+13 9.3955e+15 13642
## - TrustedYes:AgressivenessYes 1 1.8916e+13 9.3962e+15 13642
## - SPG:TrustedYes 1 2.6411e+13 9.4037e+15 13642
## - TOPG:SPG 1 2.7636e+13 9.4049e+15 13642
## - SPG:AgressivenessYes 1 3.2569e+13 9.4098e+15 13643
## - MPG:AgressivenessYes 1 3.2866e+13 9.4101e+15 13643
## - I(BPG^2) 1 3.4654e+13 9.4119e+15 13643
## - BPG:TrustedYes 1 3.8176e+13 9.4154e+15 13643
## - RPG:BPG 1 3.9598e+13 9.4168e+15 13643
## - RPG:SPG 1 4.0604e+13 9.4178e+15 13643
## <none> 9.3772e+15 13643
## - APG:AgressivenessYes 1 4.4270e+13 9.4215e+15 13643
## - MPG:BPG 1 4.4416e+13 9.4217e+15 13643
## - RPG:TrustedYes 1 4.4826e+13 9.4221e+15 13643
## - I(APG^2) 1 4.9884e+13 9.4271e+15 13643
## - MPG:TrustedYes 1 5.3431e+13 9.4307e+15 13644
## - APG:TrustedYes 1 5.3914e+13 9.4312e+15 13644
## - BPG:SPG 1 5.4901e+13 9.4321e+15 13644
## + RPG:TOPG 1 2.9549e+12 9.3743e+15 13645
## + I(RPG^2) 1 2.6680e+12 9.3746e+15 13645
## - BPG:AgressivenessYes 1 8.2840e+13 9.4601e+15 13645
## + RPG:AgressivenessYes 1 1.8519e+12 9.3754e+15 13645
## + TOPG:AgressivenessYes 1 1.5585e+12 9.3757e+15 13645
## + APG:RPG 1 1.4326e+12 9.3758e+15 13645
## + MPG:RPG 1 1.0460e+12 9.3762e+15 13645
## + I(MPG^2) 1 9.6762e+11 9.3763e+15 13645
## + APG:BPG 1 5.7952e+11 9.3767e+15 13645
## + MPG:PPG 1 1.5123e+11 9.3771e+15 13645
## + PPG:APG 1 8.1530e+10 9.3772e+15 13645
## + PPG:TrustedYes 1 3.2442e+10 9.3772e+15 13645
## + APG:TOPG 1 2.7519e+10 9.3772e+15 13645
## + TOPG:TrustedYes 1 1.5699e+10 9.3772e+15 13645
## - APG:SPG 1 8.8882e+13 9.4661e+15 13645
## - MPG:SPG 1 8.8936e+13 9.4662e+15 13645
## - PPG:TOPG 1 1.0848e+14 9.4857e+15 13646
## - TOPG:BPG 1 1.1064e+14 9.4879e+15 13646
## - PPG:SPG 1 1.3076e+14 9.5080e+15 13647
## - PPG:BPG 1 1.4755e+14 9.5248e+15 13648
## - PPG:AgressivenessYes 1 1.7077e+14 9.5480e+15 13649
## - MPG:APG 1 2.5064e+14 9.6279e+15 13653## Warning: In lm.fit(x, y, offset = offset, singular.ok = singular.ok, ...) :
## extra argument 'trControl' will be disregarded##
## Step: AIC=13641.45
## Salary17_18 ~ MPG + PPG + APG + RPG + TOPG + BPG + SPG + TrustedYes +
## AgressivenessYes + I(PPG^2) + I(APG^2) + I(TOPG^2) + I(BPG^2) +
## I(SPG^2) + MPG:APG + MPG:BPG + MPG:SPG + MPG:TrustedYes +
## MPG:AgressivenessYes + PPG:RPG + PPG:TOPG + PPG:BPG + PPG:SPG +
## PPG:AgressivenessYes + APG:SPG + APG:TrustedYes + APG:AgressivenessYes +
## RPG:BPG + RPG:SPG + RPG:TrustedYes + TOPG:BPG + TOPG:SPG +
## BPG:SPG + BPG:TrustedYes + BPG:AgressivenessYes + SPG:TrustedYes +
## SPG:AgressivenessYes + TrustedYes:AgressivenessYes
##
## Df Sum of Sq RSS AIC
## - I(SPG^2) 1 8.9867e+12 9.3937e+15 13640
## - PPG:RPG 1 1.1763e+13 9.3965e+15 13640
## - I(PPG^2) 1 1.2801e+13 9.3975e+15 13640
## - I(TOPG^2) 1 1.6978e+13 9.4017e+15 13640
## - TOPG:SPG 1 2.0354e+13 9.4051e+15 13640
## - TrustedYes:AgressivenessYes 1 2.2491e+13 9.4072e+15 13640
## - SPG:AgressivenessYes 1 2.8618e+13 9.4133e+15 13641
## - I(BPG^2) 1 3.0667e+13 9.4154e+15 13641
## - SPG:TrustedYes 1 3.1205e+13 9.4159e+15 13641
## - RPG:BPG 1 3.5295e+13 9.4200e+15 13641
## - MPG:BPG 1 3.8695e+13 9.4234e+15 13641
## <none> 9.3847e+15 13642
## - APG:AgressivenessYes 1 4.4334e+13 9.4290e+15 13642
## - RPG:SPG 1 4.5230e+13 9.4299e+15 13642
## - BPG:TrustedYes 1 4.5307e+13 9.4300e+15 13642
## - MPG:TrustedYes 1 5.0310e+13 9.4350e+15 13642
## - BPG:SPG 1 5.1866e+13 9.4366e+15 13642
## - RPG:TrustedYes 1 5.1989e+13 9.4367e+15 13642
## - MPG:AgressivenessYes 1 5.3346e+13 9.4381e+15 13642
## - APG:TrustedYes 1 5.5797e+13 9.4405e+15 13642
## - I(APG^2) 1 5.8970e+13 9.4437e+15 13642
## + MPG:TOPG 1 7.4697e+12 9.3772e+15 13643
## - BPG:AgressivenessYes 1 7.8166e+13 9.4629e+15 13643
## + TOPG:TrustedYes 1 4.0562e+12 9.3807e+15 13643
## - APG:SPG 1 8.1741e+13 9.4665e+15 13643
## + RPG:TOPG 1 3.4888e+12 9.3812e+15 13643
## + RPG:AgressivenessYes 1 2.7213e+12 9.3820e+15 13643
## + I(RPG^2) 1 2.6813e+12 9.3820e+15 13643
## + APG:BPG 1 1.5068e+12 9.3832e+15 13643
## + PPG:APG 1 1.4966e+12 9.3832e+15 13643
## + APG:TOPG 1 1.1849e+12 9.3835e+15 13643
## + MPG:PPG 1 1.1712e+12 9.3835e+15 13643
## + MPG:RPG 1 4.2411e+11 9.3843e+15 13643
## + APG:RPG 1 3.2617e+11 9.3844e+15 13643
## + TOPG:AgressivenessYes 1 2.4440e+11 9.3845e+15 13643
## + PPG:TrustedYes 1 3.5003e+10 9.3847e+15 13644
## + I(MPG^2) 1 1.2404e+10 9.3847e+15 13644
## - MPG:SPG 1 1.0616e+14 9.4909e+15 13644
## - TOPG:BPG 1 1.1080e+14 9.4955e+15 13645
## - PPG:TOPG 1 1.3397e+14 9.5187e+15 13646
## - PPG:BPG 1 1.5455e+14 9.5393e+15 13647
## - PPG:SPG 1 1.7419e+14 9.5589e+15 13648
## - PPG:AgressivenessYes 1 1.7773e+14 9.5624e+15 13648
## - MPG:APG 1 2.5526e+14 9.6400e+15 13651## Warning: In lm.fit(x, y, offset = offset, singular.ok = singular.ok, ...) :
## extra argument 'trControl' will be disregarded##
## Step: AIC=13639.88
## Salary17_18 ~ MPG + PPG + APG + RPG + TOPG + BPG + SPG + TrustedYes +
## AgressivenessYes + I(PPG^2) + I(APG^2) + I(TOPG^2) + I(BPG^2) +
## MPG:APG + MPG:BPG + MPG:SPG + MPG:TrustedYes + MPG:AgressivenessYes +
## PPG:RPG + PPG:TOPG + PPG:BPG + PPG:SPG + PPG:AgressivenessYes +
## APG:SPG + APG:TrustedYes + APG:AgressivenessYes + RPG:BPG +
## RPG:SPG + RPG:TrustedYes + TOPG:BPG + TOPG:SPG + BPG:SPG +
## BPG:TrustedYes + BPG:AgressivenessYes + SPG:TrustedYes +
## SPG:AgressivenessYes + TrustedYes:AgressivenessYes
##
## Df Sum of Sq RSS AIC
## - PPG:RPG 1 1.0154e+13 9.4039e+15 13638
## - I(PPG^2) 1 1.3888e+13 9.4076e+15 13638
## - TOPG:SPG 1 1.7597e+13 9.4113e+15 13639
## - I(TOPG^2) 1 1.9390e+13 9.4131e+15 13639
## - TrustedYes:AgressivenessYes 1 2.1834e+13 9.4155e+15 13639
## - SPG:AgressivenessYes 1 2.6160e+13 9.4199e+15 13639
## - SPG:TrustedYes 1 2.9286e+13 9.4230e+15 13639
## - I(BPG^2) 1 2.9800e+13 9.4235e+15 13639
## - RPG:BPG 1 3.4713e+13 9.4284e+15 13640
## - MPG:BPG 1 3.8838e+13 9.4325e+15 13640
## - APG:AgressivenessYes 1 4.2060e+13 9.4358e+15 13640
## <none> 9.3937e+15 13640
## - MPG:TrustedYes 1 4.4227e+13 9.4379e+15 13640
## - BPG:TrustedYes 1 4.4261e+13 9.4380e+15 13640
## - RPG:SPG 1 4.9411e+13 9.4431e+15 13640
## - RPG:TrustedYes 1 4.9504e+13 9.4432e+15 13640
## - BPG:SPG 1 4.9869e+13 9.4436e+15 13640
## - MPG:AgressivenessYes 1 5.4407e+13 9.4481e+15 13640
## - APG:TrustedYes 1 5.4503e+13 9.4482e+15 13640
## - I(APG^2) 1 5.9699e+13 9.4534e+15 13641
## - APG:SPG 1 7.2757e+13 9.4665e+15 13641
## + I(SPG^2) 1 8.9867e+12 9.3847e+15 13642
## - BPG:AgressivenessYes 1 7.7805e+13 9.4715e+15 13642
## + MPG:TOPG 1 6.8890e+12 9.3868e+15 13642
## + RPG:TOPG 1 4.4620e+12 9.3892e+15 13642
## + RPG:AgressivenessYes 1 3.1463e+12 9.3906e+15 13642
## + TOPG:TrustedYes 1 2.8438e+12 9.3909e+15 13642
## + I(RPG^2) 1 2.4070e+12 9.3913e+15 13642
## + PPG:APG 1 2.2922e+12 9.3914e+15 13642
## + APG:BPG 1 2.0728e+12 9.3916e+15 13642
## + MPG:PPG 1 1.6738e+12 9.3920e+15 13642
## + APG:TOPG 1 8.4807e+11 9.3929e+15 13642
## + MPG:RPG 1 5.2573e+11 9.3932e+15 13642
## + APG:RPG 1 4.5841e+11 9.3932e+15 13642
## + I(MPG^2) 1 1.4959e+11 9.3936e+15 13642
## + TOPG:AgressivenessYes 1 4.3040e+10 9.3937e+15 13642
## + PPG:TrustedYes 1 2.1334e+09 9.3937e+15 13642
## - MPG:SPG 1 1.0539e+14 9.4991e+15 13643
## - TOPG:BPG 1 1.0616e+14 9.4999e+15 13643
## - PPG:TOPG 1 1.3888e+14 9.5326e+15 13644
## - PPG:BPG 1 1.5303e+14 9.5467e+15 13645
## - PPG:SPG 1 1.7044e+14 9.5641e+15 13646
## - PPG:AgressivenessYes 1 1.8467e+14 9.5784e+15 13646
## - MPG:APG 1 2.4695e+14 9.6406e+15 13649## Warning: In lm.fit(x, y, offset = offset, singular.ok = singular.ok, ...) :
## extra argument 'trControl' will be disregarded##
## Step: AIC=13638.36
## Salary17_18 ~ MPG + PPG + APG + RPG + TOPG + BPG + SPG + TrustedYes +
## AgressivenessYes + I(PPG^2) + I(APG^2) + I(TOPG^2) + I(BPG^2) +
## MPG:APG + MPG:BPG + MPG:SPG + MPG:TrustedYes + MPG:AgressivenessYes +
## PPG:TOPG + PPG:BPG + PPG:SPG + PPG:AgressivenessYes + APG:SPG +
## APG:TrustedYes + APG:AgressivenessYes + RPG:BPG + RPG:SPG +
## RPG:TrustedYes + TOPG:BPG + TOPG:SPG + BPG:SPG + BPG:TrustedYes +
## BPG:AgressivenessYes + SPG:TrustedYes + SPG:AgressivenessYes +
## TrustedYes:AgressivenessYes
##
## Df Sum of Sq RSS AIC
## - I(PPG^2) 1 1.3584e+13 9.4174e+15 13637
## - TOPG:SPG 1 1.5225e+13 9.4191e+15 13637
## - TrustedYes:AgressivenessYes 1 1.9003e+13 9.4229e+15 13637
## - I(TOPG^2) 1 1.9130e+13 9.4230e+15 13637
## - SPG:AgressivenessYes 1 2.5922e+13 9.4298e+15 13638
## - SPG:TrustedYes 1 2.6378e+13 9.4302e+15 13638
## - BPG:TrustedYes 1 3.5508e+13 9.4394e+15 13638
## - I(BPG^2) 1 3.7136e+13 9.4410e+15 13638
## - RPG:TrustedYes 1 3.9366e+13 9.4432e+15 13638
## - RPG:BPG 1 4.0331e+13 9.4442e+15 13638
## <none> 9.4039e+15 13638
## - MPG:BPG 1 4.2767e+13 9.4466e+15 13638
## - APG:AgressivenessYes 1 4.3393e+13 9.4472e+15 13638
## - MPG:TrustedYes 1 4.6621e+13 9.4505e+15 13638
## - APG:TrustedYes 1 5.0702e+13 9.4546e+15 13639
## - MPG:AgressivenessYes 1 5.1574e+13 9.4554e+15 13639
## - I(APG^2) 1 5.6223e+13 9.4601e+15 13639
## - BPG:SPG 1 5.6781e+13 9.4606e+15 13639
## - APG:SPG 1 6.6475e+13 9.4703e+15 13640
## - RPG:SPG 1 6.8541e+13 9.4724e+15 13640
## + PPG:RPG 1 1.0154e+13 9.3937e+15 13640
## + MPG:TOPG 1 8.7293e+12 9.3951e+15 13640
## + I(SPG^2) 1 7.3778e+12 9.3965e+15 13640
## + MPG:RPG 1 6.4777e+12 9.3974e+15 13640
## + TOPG:TrustedYes 1 4.6333e+12 9.3992e+15 13640
## + I(RPG^2) 1 4.2090e+12 9.3996e+15 13640
## - BPG:AgressivenessYes 1 8.2144e+13 9.4860e+15 13640
## + APG:BPG 1 1.8891e+12 9.4020e+15 13640
## + PPG:APG 1 1.2012e+12 9.4027e+15 13640
## + APG:TOPG 1 9.6824e+11 9.4029e+15 13640
## + RPG:AgressivenessYes 1 9.5276e+11 9.4029e+15 13640
## + APG:RPG 1 8.0959e+11 9.4030e+15 13640
## + MPG:PPG 1 7.3736e+11 9.4031e+15 13640
## + TOPG:AgressivenessYes 1 5.5264e+11 9.4033e+15 13640
## + RPG:TOPG 1 4.2361e+11 9.4034e+15 13640
## + PPG:TrustedYes 1 7.7355e+10 9.4038e+15 13640
## + I(MPG^2) 1 2.5718e+10 9.4038e+15 13640
## - TOPG:BPG 1 1.0204e+14 9.5059e+15 13641
## - MPG:SPG 1 1.0866e+14 9.5125e+15 13641
## - PPG:TOPG 1 1.2970e+14 9.5336e+15 13642
## - PPG:BPG 1 1.5848e+14 9.5623e+15 13644
## - PPG:SPG 1 1.7050e+14 9.5744e+15 13644
## - PPG:AgressivenessYes 1 1.8071e+14 9.5846e+15 13645
## - MPG:APG 1 2.3855e+14 9.6424e+15 13647## Warning: In lm.fit(x, y, offset = offset, singular.ok = singular.ok, ...) :
## extra argument 'trControl' will be disregarded##
## Step: AIC=13636.99
## Salary17_18 ~ MPG + PPG + APG + RPG + TOPG + BPG + SPG + TrustedYes +
## AgressivenessYes + I(APG^2) + I(TOPG^2) + I(BPG^2) + MPG:APG +
## MPG:BPG + MPG:SPG + MPG:TrustedYes + MPG:AgressivenessYes +
## PPG:TOPG + PPG:BPG + PPG:SPG + PPG:AgressivenessYes + APG:SPG +
## APG:TrustedYes + APG:AgressivenessYes + RPG:BPG + RPG:SPG +
## RPG:TrustedYes + TOPG:BPG + TOPG:SPG + BPG:SPG + BPG:TrustedYes +
## BPG:AgressivenessYes + SPG:TrustedYes + SPG:AgressivenessYes +
## TrustedYes:AgressivenessYes
##
## Df Sum of Sq RSS AIC
## - I(TOPG^2) 1 8.6971e+12 9.4261e+15 13635
## - TOPG:SPG 1 9.3615e+12 9.4268e+15 13635
## - TrustedYes:AgressivenessYes 1 1.6538e+13 9.4340e+15 13636
## - SPG:AgressivenessYes 1 2.2735e+13 9.4402e+15 13636
## - SPG:TrustedYes 1 2.4066e+13 9.4415e+15 13636
## - BPG:TrustedYes 1 3.4595e+13 9.4520e+15 13637
## - RPG:TrustedYes 1 3.4677e+13 9.4521e+15 13637
## - I(BPG^2) 1 3.5401e+13 9.4528e+15 13637
## - MPG:BPG 1 3.5757e+13 9.4532e+15 13637
## - APG:AgressivenessYes 1 3.9189e+13 9.4566e+15 13637
## - RPG:BPG 1 4.0363e+13 9.4578e+15 13637
## <none> 9.4174e+15 13637
## - BPG:SPG 1 4.8450e+13 9.4659e+15 13637
## - APG:TrustedYes 1 4.9277e+13 9.4667e+15 13637
## - MPG:AgressivenessYes 1 5.4159e+13 9.4716e+15 13638
## - I(APG^2) 1 5.6316e+13 9.4738e+15 13638
## - APG:SPG 1 5.7806e+13 9.4752e+15 13638
## - MPG:TrustedYes 1 6.4012e+13 9.4815e+15 13638
## - RPG:SPG 1 6.4351e+13 9.4818e+15 13638
## + I(PPG^2) 1 1.3584e+13 9.4039e+15 13638
## + PPG:RPG 1 9.8506e+12 9.4076e+15 13638
## + MPG:TOPG 1 8.9714e+12 9.4085e+15 13639
## - BPG:AgressivenessYes 1 7.7034e+13 9.4945e+15 13639
## + I(SPG^2) 1 8.3750e+12 9.4091e+15 13639
## + MPG:RPG 1 6.1670e+12 9.4113e+15 13639
## + TOPG:TrustedYes 1 5.7008e+12 9.4117e+15 13639
## + MPG:PPG 1 4.4749e+12 9.4130e+15 13639
## + I(RPG^2) 1 2.8331e+12 9.4146e+15 13639
## + APG:BPG 1 2.2905e+12 9.4151e+15 13639
## + APG:TOPG 1 2.0427e+12 9.4154e+15 13639
## + PPG:TrustedYes 1 1.8596e+12 9.4156e+15 13639
## + RPG:AgressivenessYes 1 1.5035e+12 9.4159e+15 13639
## + APG:RPG 1 9.7131e+11 9.4165e+15 13639
## + PPG:APG 1 7.3870e+11 9.4167e+15 13639
## + TOPG:AgressivenessYes 1 6.5417e+11 9.4168e+15 13639
## + I(MPG^2) 1 6.5016e+11 9.4168e+15 13639
## + RPG:TOPG 1 2.3035e+11 9.4172e+15 13639
## - TOPG:BPG 1 9.1419e+13 9.5089e+15 13639
## - MPG:SPG 1 1.0795e+14 9.5254e+15 13640
## - PPG:BPG 1 1.4584e+14 9.5633e+15 13642
## - PPG:TOPG 1 1.4671e+14 9.5641e+15 13642
## - PPG:AgressivenessYes 1 1.8491e+14 9.6024e+15 13644
## - PPG:SPG 1 1.8553e+14 9.6030e+15 13644
## - MPG:APG 1 2.2637e+14 9.6438e+15 13646## Warning: In lm.fit(x, y, offset = offset, singular.ok = singular.ok, ...) :
## extra argument 'trControl' will be disregarded##
## Step: AIC=13635.4
## Salary17_18 ~ MPG + PPG + APG + RPG + TOPG + BPG + SPG + TrustedYes +
## AgressivenessYes + I(APG^2) + I(BPG^2) + MPG:APG + MPG:BPG +
## MPG:SPG + MPG:TrustedYes + MPG:AgressivenessYes + PPG:TOPG +
## PPG:BPG + PPG:SPG + PPG:AgressivenessYes + APG:SPG + APG:TrustedYes +
## APG:AgressivenessYes + RPG:BPG + RPG:SPG + RPG:TrustedYes +
## TOPG:BPG + TOPG:SPG + BPG:SPG + BPG:TrustedYes + BPG:AgressivenessYes +
## SPG:TrustedYes + SPG:AgressivenessYes + TrustedYes:AgressivenessYes
##
## Df Sum of Sq RSS AIC
## - TOPG:SPG 1 1.5012e+13 9.4411e+15 13634
## - TrustedYes:AgressivenessYes 1 1.8077e+13 9.4442e+15 13634
## - SPG:TrustedYes 1 2.3028e+13 9.4492e+15 13634
## - SPG:AgressivenessYes 1 2.6291e+13 9.4524e+15 13635
## - I(BPG^2) 1 3.0514e+13 9.4567e+15 13635
## - MPG:BPG 1 3.1698e+13 9.4578e+15 13635
## - RPG:TrustedYes 1 3.3352e+13 9.4595e+15 13635
## - RPG:BPG 1 3.5502e+13 9.4616e+15 13635
## - BPG:TrustedYes 1 3.6919e+13 9.4631e+15 13635
## - APG:AgressivenessYes 1 3.7283e+13 9.4634e+15 13635
## <none> 9.4261e+15 13635
## - BPG:SPG 1 4.6076e+13 9.4722e+15 13636
## - APG:TrustedYes 1 4.7847e+13 9.4740e+15 13636
## - MPG:AgressivenessYes 1 5.0666e+13 9.4768e+15 13636
## - RPG:SPG 1 6.3013e+13 9.4891e+15 13636
## - MPG:TrustedYes 1 6.4020e+13 9.4902e+15 13636
## - APG:SPG 1 6.7654e+13 9.4938e+15 13637
## - BPG:AgressivenessYes 1 7.4084e+13 9.5002e+15 13637
## + APG:TOPG 1 1.0125e+13 9.4160e+15 13637
## + PPG:RPG 1 9.7857e+12 9.4164e+15 13637
## + I(SPG^2) 1 9.6484e+12 9.4165e+15 13637
## + I(TOPG^2) 1 8.6971e+12 9.4174e+15 13637
## + MPG:TOPG 1 7.5906e+12 9.4185e+15 13637
## + MPG:RPG 1 6.6445e+12 9.4195e+15 13637
## + APG:BPG 1 4.5401e+12 9.4216e+15 13637
## + I(PPG^2) 1 3.1517e+12 9.4230e+15 13637
## + APG:RPG 1 2.9478e+12 9.4232e+15 13637
## + I(RPG^2) 1 2.2983e+12 9.4238e+15 13637
## + TOPG:TrustedYes 1 2.0447e+12 9.4241e+15 13637
## + RPG:AgressivenessYes 1 1.3890e+12 9.4247e+15 13637
## + PPG:TrustedYes 1 1.2379e+12 9.4249e+15 13637
## + MPG:PPG 1 1.0469e+12 9.4251e+15 13637
## + RPG:TOPG 1 9.9156e+11 9.4251e+15 13637
## + TOPG:AgressivenessYes 1 5.0245e+11 9.4256e+15 13637
## + PPG:APG 1 2.9068e+11 9.4258e+15 13637
## + I(MPG^2) 1 2.3176e+11 9.4259e+15 13637
## - I(APG^2) 1 9.2197e+13 9.5183e+15 13638
## - TOPG:BPG 1 9.4239e+13 9.5204e+15 13638
## - MPG:SPG 1 1.0094e+14 9.5271e+15 13638
## - PPG:BPG 1 1.4670e+14 9.5728e+15 13640
## - PPG:SPG 1 1.7721e+14 9.6034e+15 13642
## - PPG:AgressivenessYes 1 1.8557e+14 9.6117e+15 13642
## - MPG:APG 1 2.1799e+14 9.6441e+15 13644
## - PPG:TOPG 1 2.6228e+14 9.6884e+15 13646## Warning: In lm.fit(x, y, offset = offset, singular.ok = singular.ok, ...) :
## extra argument 'trControl' will be disregarded##
## Step: AIC=13634.1
## Salary17_18 ~ MPG + PPG + APG + RPG + TOPG + BPG + SPG + TrustedYes +
## AgressivenessYes + I(APG^2) + I(BPG^2) + MPG:APG + MPG:BPG +
## MPG:SPG + MPG:TrustedYes + MPG:AgressivenessYes + PPG:TOPG +
## PPG:BPG + PPG:SPG + PPG:AgressivenessYes + APG:SPG + APG:TrustedYes +
## APG:AgressivenessYes + RPG:BPG + RPG:SPG + RPG:TrustedYes +
## TOPG:BPG + BPG:SPG + BPG:TrustedYes + BPG:AgressivenessYes +
## SPG:TrustedYes + SPG:AgressivenessYes + TrustedYes:AgressivenessYes
##
## Df Sum of Sq RSS AIC
## - SPG:AgressivenessYes 1 1.4402e+13 9.4555e+15 13633
## - TrustedYes:AgressivenessYes 1 1.8134e+13 9.4593e+15 13633
## - SPG:TrustedYes 1 2.3015e+13 9.4642e+15 13633
## - RPG:TrustedYes 1 3.2760e+13 9.4739e+15 13634
## - MPG:BPG 1 3.3229e+13 9.4744e+15 13634
## - BPG:TrustedYes 1 3.4140e+13 9.4753e+15 13634
## - I(BPG^2) 1 3.4493e+13 9.4756e+15 13634
## - RPG:BPG 1 3.6872e+13 9.4780e+15 13634
## - APG:AgressivenessYes 1 3.9295e+13 9.4804e+15 13634
## - BPG:SPG 1 3.9715e+13 9.4809e+15 13634
## <none> 9.4411e+15 13634
## - MPG:AgressivenessYes 1 4.5109e+13 9.4863e+15 13634
## - APG:TrustedYes 1 4.8019e+13 9.4892e+15 13634
## - APG:SPG 1 5.2745e+13 9.4939e+15 13635
## - MPG:TrustedYes 1 6.0150e+13 9.5013e+15 13635
## - RPG:SPG 1 6.3186e+13 9.5043e+15 13635
## + APG:TOPG 1 1.6858e+13 9.4243e+15 13635
## + TOPG:SPG 1 1.5012e+13 9.4261e+15 13635
## + I(TOPG^2) 1 1.4347e+13 9.4268e+15 13635
## - BPG:AgressivenessYes 1 7.3441e+13 9.5146e+15 13636
## + PPG:RPG 1 7.3922e+12 9.4338e+15 13636
## + APG:BPG 1 7.3841e+12 9.4338e+15 13636
## + I(SPG^2) 1 7.1170e+12 9.4340e+15 13636
## + MPG:RPG 1 4.7193e+12 9.4364e+15 13636
## + TOPG:AgressivenessYes 1 2.8318e+12 9.4383e+15 13636
## + I(RPG^2) 1 2.4937e+12 9.4387e+15 13636
## + APG:RPG 1 1.5702e+12 9.4396e+15 13636
## + RPG:AgressivenessYes 1 1.1306e+12 9.4400e+15 13636
## + RPG:TOPG 1 7.7978e+11 9.4404e+15 13636
## + PPG:TrustedYes 1 7.0591e+11 9.4404e+15 13636
## + MPG:TOPG 1 2.5689e+11 9.4409e+15 13636
## + PPG:APG 1 2.2651e+11 9.4409e+15 13636
## + I(MPG^2) 1 2.0873e+11 9.4409e+15 13636
## + I(PPG^2) 1 1.3335e+11 9.4410e+15 13636
## + MPG:PPG 1 6.8860e+10 9.4411e+15 13636
## + TOPG:TrustedYes 1 4.5390e+10 9.4411e+15 13636
## - TOPG:BPG 1 9.4280e+13 9.5354e+15 13636
## - MPG:SPG 1 9.6649e+13 9.5378e+15 13637
## - I(APG^2) 1 9.7437e+13 9.5386e+15 13637
## - PPG:BPG 1 1.5195e+14 9.5931e+15 13639
## - PPG:AgressivenessYes 1 1.7062e+14 9.6118e+15 13640
## - PPG:SPG 1 2.0365e+14 9.6448e+15 13642
## - MPG:APG 1 2.0611e+14 9.6473e+15 13642
## - PPG:TOPG 1 2.9848e+14 9.7396e+15 13646## Warning: In lm.fit(x, y, offset = offset, singular.ok = singular.ok, ...) :
## extra argument 'trControl' will be disregarded##
## Step: AIC=13632.78
## Salary17_18 ~ MPG + PPG + APG + RPG + TOPG + BPG + SPG + TrustedYes +
## AgressivenessYes + I(APG^2) + I(BPG^2) + MPG:APG + MPG:BPG +
## MPG:SPG + MPG:TrustedYes + MPG:AgressivenessYes + PPG:TOPG +
## PPG:BPG + PPG:SPG + PPG:AgressivenessYes + APG:SPG + APG:TrustedYes +
## APG:AgressivenessYes + RPG:BPG + RPG:SPG + RPG:TrustedYes +
## TOPG:BPG + BPG:SPG + BPG:TrustedYes + BPG:AgressivenessYes +
## SPG:TrustedYes + TrustedYes:AgressivenessYes
##
## Df Sum of Sq RSS AIC
## - SPG:TrustedYes 1 1.6046e+13 9.4716e+15 13632
## - TrustedYes:AgressivenessYes 1 1.9932e+13 9.4755e+15 13632
## - RPG:TrustedYes 1 2.9881e+13 9.4854e+15 13632
## - BPG:TrustedYes 1 3.2438e+13 9.4880e+15 13632
## - I(BPG^2) 1 3.3961e+13 9.4895e+15 13632
## - MPG:BPG 1 3.5868e+13 9.4914e+15 13632
## - RPG:BPG 1 3.6535e+13 9.4921e+15 13632
## - BPG:SPG 1 3.9482e+13 9.4950e+15 13633
## - APG:TrustedYes 1 4.2013e+13 9.4976e+15 13633
## <none> 9.4555e+15 13633
## - RPG:SPG 1 5.5233e+13 9.5108e+15 13633
## - APG:AgressivenessYes 1 5.7219e+13 9.5128e+15 13633
## - MPG:TrustedYes 1 6.8356e+13 9.5239e+15 13634
## + APG:TOPG 1 1.7180e+13 9.4384e+15 13634
## + I(TOPG^2) 1 1.4408e+13 9.4411e+15 13634
## + SPG:AgressivenessYes 1 1.4402e+13 9.4411e+15 13634
## - BPG:AgressivenessYes 1 7.3733e+13 9.5293e+15 13634
## + APG:BPG 1 8.7318e+12 9.4468e+15 13634
## + PPG:RPG 1 8.2999e+12 9.4472e+15 13634
## + I(SPG^2) 1 6.4103e+12 9.4491e+15 13634
## + MPG:RPG 1 6.3194e+12 9.4492e+15 13634
## - MPG:AgressivenessYes 1 8.2039e+13 9.5376e+15 13635
## + TOPG:SPG 1 3.1225e+12 9.4524e+15 13635
## + I(RPG^2) 1 2.7494e+12 9.4528e+15 13635
## + APG:RPG 1 2.6404e+12 9.4529e+15 13635
## + TOPG:AgressivenessYes 1 2.3385e+12 9.4532e+15 13635
## + RPG:AgressivenessYes 1 1.3166e+12 9.4542e+15 13635
## + RPG:TOPG 1 9.6928e+11 9.4546e+15 13635
## + I(MPG^2) 1 7.0147e+11 9.4548e+15 13635
## + MPG:TOPG 1 6.8054e+11 9.4549e+15 13635
## + PPG:TrustedYes 1 4.0062e+11 9.4551e+15 13635
## + PPG:APG 1 2.3185e+11 9.4553e+15 13635
## + I(PPG^2) 1 2.0990e+11 9.4553e+15 13635
## + TOPG:TrustedYes 1 2.0699e+11 9.4553e+15 13635
## + MPG:PPG 1 2.0371e+11 9.4553e+15 13635
## - MPG:SPG 1 8.9027e+13 9.5446e+15 13635
## - TOPG:BPG 1 9.4830e+13 9.5504e+15 13635
## - APG:SPG 1 9.8870e+13 9.5544e+15 13635
## - I(APG^2) 1 1.2518e+14 9.5807e+15 13637
## - PPG:BPG 1 1.5397e+14 9.6095e+15 13638
## - PPG:SPG 1 1.8981e+14 9.6454e+15 13640
## - PPG:AgressivenessYes 1 2.0890e+14 9.6644e+15 13640
## - MPG:APG 1 2.1935e+14 9.6749e+15 13641
## - PPG:TOPG 1 3.0342e+14 9.7590e+15 13645## Warning: In lm.fit(x, y, offset = offset, singular.ok = singular.ok, ...) :
## extra argument 'trControl' will be disregarded##
## Step: AIC=13631.53
## Salary17_18 ~ MPG + PPG + APG + RPG + TOPG + BPG + SPG + TrustedYes +
## AgressivenessYes + I(APG^2) + I(BPG^2) + MPG:APG + MPG:BPG +
## MPG:SPG + MPG:TrustedYes + MPG:AgressivenessYes + PPG:TOPG +
## PPG:BPG + PPG:SPG + PPG:AgressivenessYes + APG:SPG + APG:TrustedYes +
## APG:AgressivenessYes + RPG:BPG + RPG:SPG + RPG:TrustedYes +
## TOPG:BPG + BPG:SPG + BPG:TrustedYes + BPG:AgressivenessYes +
## TrustedYes:AgressivenessYes
##
## Df Sum of Sq RSS AIC
## - TrustedYes:AgressivenessYes 1 1.9177e+13 9.4908e+15 13630
## - MPG:BPG 1 2.9605e+13 9.5012e+15 13631
## - APG:TrustedYes 1 3.0399e+13 9.5020e+15 13631
## - RPG:TrustedYes 1 3.3813e+13 9.5054e+15 13631
## - I(BPG^2) 1 3.4829e+13 9.5064e+15 13631
## - RPG:BPG 1 3.5759e+13 9.5074e+15 13631
## <none> 9.4716e+15 13632
## - BPG:SPG 1 4.4801e+13 9.5164e+15 13632
## - BPG:TrustedYes 1 4.6437e+13 9.5180e+15 13632
## - APG:AgressivenessYes 1 6.0279e+13 9.5319e+15 13632
## - RPG:SPG 1 6.3998e+13 9.5356e+15 13632
## - MPG:TrustedYes 1 6.4673e+13 9.5363e+15 13632
## + APG:TOPG 1 1.9547e+13 9.4520e+15 13633
## + SPG:TrustedYes 1 1.6046e+13 9.4555e+15 13633
## + I(TOPG^2) 1 1.3255e+13 9.4583e+15 13633
## - BPG:AgressivenessYes 1 7.3173e+13 9.5448e+15 13633
## + APG:BPG 1 1.1107e+13 9.4605e+15 13633
## + SPG:AgressivenessYes 1 7.4323e+12 9.4642e+15 13633
## - MPG:AgressivenessYes 1 7.9053e+13 9.5506e+15 13633
## - MPG:SPG 1 7.9087e+13 9.5507e+15 13633
## + PPG:RPG 1 5.9630e+12 9.4656e+15 13633
## + I(SPG^2) 1 5.3769e+12 9.4662e+15 13633
## + TOPG:SPG 1 4.8149e+12 9.4668e+15 13633
## + MPG:RPG 1 2.9857e+12 9.4686e+15 13633
## + I(RPG^2) 1 2.5954e+12 9.4690e+15 13633
## + TOPG:AgressivenessYes 1 2.3946e+12 9.4692e+15 13633
## + APG:RPG 1 2.2360e+12 9.4694e+15 13633
## + MPG:TOPG 1 1.5167e+12 9.4701e+15 13634
## + RPG:AgressivenessYes 1 1.3951e+12 9.4702e+15 13634
## + RPG:TOPG 1 5.1049e+11 9.4711e+15 13634
## + I(MPG^2) 1 5.0903e+11 9.4711e+15 13634
## + PPG:TrustedYes 1 3.9874e+11 9.4712e+15 13634
## + TOPG:TrustedYes 1 1.9127e+11 9.4714e+15 13634
## + I(PPG^2) 1 8.0207e+10 9.4715e+15 13634
## + MPG:PPG 1 4.0493e+10 9.4716e+15 13634
## + PPG:APG 1 3.3653e+10 9.4716e+15 13634
## - APG:SPG 1 8.9265e+13 9.5609e+15 13634
## - TOPG:BPG 1 8.9852e+13 9.5614e+15 13634
## - I(APG^2) 1 1.1967e+14 9.5913e+15 13635
## - PPG:BPG 1 1.4804e+14 9.6196e+15 13636
## - PPG:SPG 1 1.7773e+14 9.6493e+15 13638
## - MPG:APG 1 2.0338e+14 9.6750e+15 13639
## - PPG:AgressivenessYes 1 2.0830e+14 9.6799e+15 13639
## - PPG:TOPG 1 2.9161e+14 9.7632e+15 13643## Warning: In lm.fit(x, y, offset = offset, singular.ok = singular.ok, ...) :
## extra argument 'trControl' will be disregarded##
## Step: AIC=13630.42
## Salary17_18 ~ MPG + PPG + APG + RPG + TOPG + BPG + SPG + TrustedYes +
## AgressivenessYes + I(APG^2) + I(BPG^2) + MPG:APG + MPG:BPG +
## MPG:SPG + MPG:TrustedYes + MPG:AgressivenessYes + PPG:TOPG +
## PPG:BPG + PPG:SPG + PPG:AgressivenessYes + APG:SPG + APG:TrustedYes +
## APG:AgressivenessYes + RPG:BPG + RPG:SPG + RPG:TrustedYes +
## TOPG:BPG + BPG:SPG + BPG:TrustedYes + BPG:AgressivenessYes
##
## Df Sum of Sq RSS AIC
## - APG:TrustedYes 1 1.4432e+13 9.5052e+15 13629
## - MPG:BPG 1 2.3509e+13 9.5143e+15 13630
## - RPG:TrustedYes 1 2.5607e+13 9.5164e+15 13630
## - I(BPG^2) 1 3.0619e+13 9.5214e+15 13630
## - RPG:BPG 1 3.2248e+13 9.5230e+15 13630
## - BPG:SPG 1 4.0005e+13 9.5308e+15 13630
## <none> 9.4908e+15 13630
## - MPG:TrustedYes 1 4.9139e+13 9.5399e+15 13631
## - RPG:SPG 1 5.6879e+13 9.5477e+15 13631
## - BPG:TrustedYes 1 5.7983e+13 9.5488e+15 13631
## + APG:TOPG 1 2.4266e+13 9.4665e+15 13631
## - MPG:AgressivenessYes 1 6.4833e+13 9.5556e+15 13631
## + TrustedYes:AgressivenessYes 1 1.9177e+13 9.4716e+15 13632
## + SPG:TrustedYes 1 1.5292e+13 9.4755e+15 13632
## + I(TOPG^2) 1 1.5178e+13 9.4756e+15 13632
## + APG:BPG 1 1.5009e+13 9.4758e+15 13632
## - APG:AgressivenessYes 1 7.1690e+13 9.5625e+15 13632
## - MPG:SPG 1 7.4333e+13 9.5651e+15 13632
## + SPG:AgressivenessYes 1 8.8120e+12 9.4820e+15 13632
## + I(SPG^2) 1 5.0718e+12 9.4857e+15 13632
## - BPG:AgressivenessYes 1 8.1817e+13 9.5726e+15 13632
## + TOPG:SPG 1 4.3569e+12 9.4864e+15 13632
## + PPG:RPG 1 3.9603e+12 9.4868e+15 13632
## + MPG:TOPG 1 2.7634e+12 9.4880e+15 13632
## + TOPG:AgressivenessYes 1 2.5217e+12 9.4883e+15 13632
## + APG:RPG 1 2.1348e+12 9.4886e+15 13632
## + RPG:AgressivenessYes 1 2.0987e+12 9.4887e+15 13632
## + I(RPG^2) 1 2.0583e+12 9.4887e+15 13632
## + PPG:TrustedYes 1 1.9276e+12 9.4888e+15 13632
## + I(MPG^2) 1 1.5681e+12 9.4892e+15 13632
## + TOPG:TrustedYes 1 1.3145e+12 9.4895e+15 13632
## + MPG:RPG 1 7.9818e+11 9.4900e+15 13632
## + PPG:APG 1 6.9926e+11 9.4901e+15 13632
## + MPG:PPG 1 6.4178e+11 9.4901e+15 13632
## + RPG:TOPG 1 1.9058e+11 9.4906e+15 13632
## + I(PPG^2) 1 1.7251e+10 9.4908e+15 13632
## - TOPG:BPG 1 8.8664e+13 9.5794e+15 13632
## - APG:SPG 1 9.5817e+13 9.5866e+15 13633
## - I(APG^2) 1 1.3008e+14 9.6209e+15 13634
## - PPG:BPG 1 1.4535e+14 9.6361e+15 13635
## - PPG:SPG 1 1.7703e+14 9.6678e+15 13637
## - MPG:APG 1 1.8438e+14 9.6752e+15 13637
## - PPG:AgressivenessYes 1 2.0100e+14 9.6918e+15 13638
## - PPG:TOPG 1 2.8905e+14 9.7798e+15 13642## Warning: In lm.fit(x, y, offset = offset, singular.ok = singular.ok, ...) :
## extra argument 'trControl' will be disregarded##
## Step: AIC=13629.09
## Salary17_18 ~ MPG + PPG + APG + RPG + TOPG + BPG + SPG + TrustedYes +
## AgressivenessYes + I(APG^2) + I(BPG^2) + MPG:APG + MPG:BPG +
## MPG:SPG + MPG:TrustedYes + MPG:AgressivenessYes + PPG:TOPG +
## PPG:BPG + PPG:SPG + PPG:AgressivenessYes + APG:SPG + APG:AgressivenessYes +
## RPG:BPG + RPG:SPG + RPG:TrustedYes + TOPG:BPG + BPG:SPG +
## BPG:TrustedYes + BPG:AgressivenessYes
##
## Df Sum of Sq RSS AIC
## - RPG:TrustedYes 1 2.0596e+13 9.5258e+15 13628
## - MPG:BPG 1 2.2941e+13 9.5281e+15 13628
## - I(BPG^2) 1 3.0927e+13 9.5361e+15 13628
## - RPG:BPG 1 3.2124e+13 9.5373e+15 13629
## - BPG:SPG 1 3.7257e+13 9.5425e+15 13629
## <none> 9.5052e+15 13629
## - RPG:SPG 1 5.3024e+13 9.5582e+15 13630
## - MPG:TrustedYes 1 5.4952e+13 9.5602e+15 13630
## + APG:TOPG 1 2.6871e+13 9.4783e+15 13630
## + APG:BPG 1 1.7806e+13 9.4874e+15 13630
## - BPG:TrustedYes 1 6.8977e+13 9.5742e+15 13630
## + APG:TrustedYes 1 1.4432e+13 9.4908e+15 13630
## + I(TOPG^2) 1 1.3270e+13 9.4919e+15 13630
## - MPG:AgressivenessYes 1 7.3350e+13 9.5786e+15 13630
## - MPG:SPG 1 7.5699e+13 9.5809e+15 13631
## + SPG:AgressivenessYes 1 6.5674e+12 9.4986e+15 13631
## + SPG:TrustedYes 1 5.5935e+12 9.4996e+15 13631
## + TOPG:SPG 1 5.1739e+12 9.5000e+15 13631
## + I(SPG^2) 1 5.1047e+12 9.5001e+15 13631
## + PPG:RPG 1 3.6801e+12 9.5015e+15 13631
## + TrustedYes:AgressivenessYes 1 3.2111e+12 9.5020e+15 13631
## + RPG:AgressivenessYes 1 2.5533e+12 9.5027e+15 13631
## + PPG:APG 1 2.0066e+12 9.5032e+15 13631
## + MPG:TOPG 1 1.8904e+12 9.5033e+15 13631
## + APG:RPG 1 1.7628e+12 9.5034e+15 13631
## + I(RPG^2) 1 1.7020e+12 9.5035e+15 13631
## + TOPG:AgressivenessYes 1 1.4031e+12 9.5038e+15 13631
## + PPG:TrustedYes 1 1.2741e+12 9.5039e+15 13631
## + MPG:RPG 1 1.0870e+12 9.5041e+15 13631
## + TOPG:TrustedYes 1 1.0840e+12 9.5041e+15 13631
## + I(MPG^2) 1 1.0038e+11 9.5051e+15 13631
## + RPG:TOPG 1 3.0586e+10 9.5052e+15 13631
## + I(PPG^2) 1 9.3618e+09 9.5052e+15 13631
## + MPG:PPG 1 9.0375e+09 9.5052e+15 13631
## - TOPG:BPG 1 8.9234e+13 9.5944e+15 13631
## - APG:SPG 1 9.1849e+13 9.5971e+15 13631
## - BPG:AgressivenessYes 1 9.6423e+13 9.6016e+15 13632
## - APG:AgressivenessYes 1 1.3083e+14 9.6360e+15 13633
## - I(APG^2) 1 1.3155e+14 9.6368e+15 13633
## - PPG:BPG 1 1.4868e+14 9.6539e+15 13634
## - MPG:APG 1 1.7187e+14 9.6771e+15 13635
## - PPG:SPG 1 1.8236e+14 9.6876e+15 13636
## - PPG:AgressivenessYes 1 1.9657e+14 9.7018e+15 13636
## - PPG:TOPG 1 2.7771e+14 9.7829e+15 13640## Warning: In lm.fit(x, y, offset = offset, singular.ok = singular.ok, ...) :
## extra argument 'trControl' will be disregarded##
## Step: AIC=13628.05
## Salary17_18 ~ MPG + PPG + APG + RPG + TOPG + BPG + SPG + TrustedYes +
## AgressivenessYes + I(APG^2) + I(BPG^2) + MPG:APG + MPG:BPG +
## MPG:SPG + MPG:TrustedYes + MPG:AgressivenessYes + PPG:TOPG +
## PPG:BPG + PPG:SPG + PPG:AgressivenessYes + APG:SPG + APG:AgressivenessYes +
## RPG:BPG + RPG:SPG + TOPG:BPG + BPG:SPG + BPG:TrustedYes +
## BPG:AgressivenessYes
##
## Df Sum of Sq RSS AIC
## - RPG:BPG 1 2.4080e+13 9.5499e+15 13627
## - MPG:BPG 1 2.5603e+13 9.5514e+15 13627
## - I(BPG^2) 1 2.6794e+13 9.5526e+15 13627
## - BPG:SPG 1 2.8418e+13 9.5542e+15 13627
## - RPG:SPG 1 3.5206e+13 9.5610e+15 13628
## - MPG:TrustedYes 1 4.0444e+13 9.5662e+15 13628
## <none> 9.5258e+15 13628
## - BPG:TrustedYes 1 4.8696e+13 9.5745e+15 13628
## + APG:TOPG 1 2.4951e+13 9.5009e+15 13629
## - MPG:SPG 1 6.2779e+13 9.5886e+15 13629
## + RPG:TrustedYes 1 2.0596e+13 9.5052e+15 13629
## + RPG:AgressivenessYes 1 1.5498e+13 9.5103e+15 13629
## + APG:BPG 1 1.3015e+13 9.5128e+15 13629
## - MPG:AgressivenessYes 1 7.4532e+13 9.6003e+15 13630
## + I(TOPG^2) 1 1.1670e+13 9.5141e+15 13630
## + APG:TrustedYes 1 9.4218e+12 9.5164e+15 13630
## + SPG:TrustedYes 1 8.7424e+12 9.5171e+15 13630
## + MPG:RPG 1 7.2499e+12 9.5186e+15 13630
## + TOPG:SPG 1 5.7435e+12 9.5201e+15 13630
## + SPG:AgressivenessYes 1 4.6596e+12 9.5211e+15 13630
## + I(SPG^2) 1 4.3883e+12 9.5214e+15 13630
## + MPG:TOPG 1 3.5320e+12 9.5223e+15 13630
## + TOPG:TrustedYes 1 2.5560e+12 9.5232e+15 13630
## + TrustedYes:AgressivenessYes 1 1.8627e+12 9.5239e+15 13630
## + PPG:APG 1 1.8435e+12 9.5240e+15 13630
## + RPG:TOPG 1 1.7163e+12 9.5241e+15 13630
## + I(RPG^2) 1 8.1937e+11 9.5250e+15 13630
## + MPG:PPG 1 3.5216e+11 9.5254e+15 13630
## + I(MPG^2) 1 3.1239e+11 9.5255e+15 13630
## + TOPG:AgressivenessYes 1 2.7606e+11 9.5255e+15 13630
## + APG:RPG 1 1.7304e+11 9.5256e+15 13630
## + PPG:RPG 1 6.3383e+10 9.5257e+15 13630
## + I(PPG^2) 1 4.9227e+10 9.5258e+15 13630
## + PPG:TrustedYes 1 3.4592e+10 9.5258e+15 13630
## - BPG:AgressivenessYes 1 8.9921e+13 9.6157e+15 13630
## - TOPG:BPG 1 9.1722e+13 9.6175e+15 13630
## - APG:SPG 1 1.0066e+14 9.6265e+15 13631
## - APG:AgressivenessYes 1 1.1728e+14 9.6431e+15 13632
## - I(APG^2) 1 1.3300e+14 9.6588e+15 13632
## - PPG:BPG 1 1.4617e+14 9.6720e+15 13633
## - MPG:APG 1 1.7249e+14 9.6983e+15 13634
## - PPG:SPG 1 1.8130e+14 9.7071e+15 13634
## - PPG:AgressivenessYes 1 1.9227e+14 9.7181e+15 13635
## - PPG:TOPG 1 2.8196e+14 9.8078e+15 13639## Warning: In lm.fit(x, y, offset = offset, singular.ok = singular.ok, ...) :
## extra argument 'trControl' will be disregarded##
## Step: AIC=13627.17
## Salary17_18 ~ MPG + PPG + APG + RPG + TOPG + BPG + SPG + TrustedYes +
## AgressivenessYes + I(APG^2) + I(BPG^2) + MPG:APG + MPG:BPG +
## MPG:SPG + MPG:TrustedYes + MPG:AgressivenessYes + PPG:TOPG +
## PPG:BPG + PPG:SPG + PPG:AgressivenessYes + APG:SPG + APG:AgressivenessYes +
## RPG:SPG + TOPG:BPG + BPG:SPG + BPG:TrustedYes + BPG:AgressivenessYes
##
## Df Sum of Sq RSS AIC
## - I(BPG^2) 1 8.4322e+12 9.5583e+15 13626
## - BPG:SPG 1 3.7370e+13 9.5873e+15 13627
## - RPG:SPG 1 4.3118e+13 9.5930e+15 13627
## - BPG:TrustedYes 1 4.3296e+13 9.5932e+15 13627
## <none> 9.5499e+15 13627
## - MPG:TrustedYes 1 4.4260e+13 9.5941e+15 13627
## - MPG:BPG 1 5.1604e+13 9.6015e+15 13628
## + RPG:BPG 1 2.4080e+13 9.5258e+15 13628
## + APG:TOPG 1 1.7511e+13 9.5324e+15 13628
## - MPG:AgressivenessYes 1 6.9521e+13 9.6194e+15 13628
## + RPG:TrustedYes 1 1.2552e+13 9.5373e+15 13629
## + I(RPG^2) 1 1.0216e+13 9.5397e+15 13629
## + APG:TrustedYes 1 1.0208e+13 9.5397e+15 13629
## + RPG:AgressivenessYes 1 8.8331e+12 9.5410e+15 13629
## - MPG:SPG 1 7.8034e+13 9.6279e+15 13629
## + SPG:TrustedYes 1 7.6445e+12 9.5422e+15 13629
## + I(TOPG^2) 1 7.1081e+12 9.5428e+15 13629
## + TOPG:SPG 1 6.3194e+12 9.5436e+15 13629
## + SPG:AgressivenessYes 1 4.8610e+12 9.5450e+15 13629
## + APG:BPG 1 4.7501e+12 9.5451e+15 13629
## + I(SPG^2) 1 3.7010e+12 9.5462e+15 13629
## + TOPG:TrustedYes 1 2.8915e+12 9.5470e+15 13629
## + APG:RPG 1 1.8279e+12 9.5481e+15 13629
## + TrustedYes:AgressivenessYes 1 1.3202e+12 9.5486e+15 13629
## + MPG:TOPG 1 1.1767e+12 9.5487e+15 13629
## + MPG:RPG 1 8.7588e+11 9.5490e+15 13629
## + PPG:APG 1 7.5660e+11 9.5491e+15 13629
## + PPG:RPG 1 5.5608e+11 9.5493e+15 13629
## + TOPG:AgressivenessYes 1 3.8793e+11 9.5495e+15 13629
## + RPG:TOPG 1 3.8586e+11 9.5495e+15 13629
## + I(MPG^2) 1 8.8105e+10 9.5498e+15 13629
## + I(PPG^2) 1 4.1152e+10 9.5498e+15 13629
## + MPG:PPG 1 1.2955e+10 9.5499e+15 13629
## + PPG:TrustedYes 1 1.2069e+10 9.5499e+15 13629
## - BPG:AgressivenessYes 1 8.6883e+13 9.6368e+15 13629
## - TOPG:BPG 1 9.9227e+13 9.6491e+15 13630
## - APG:SPG 1 1.0627e+14 9.6562e+15 13630
## - APG:AgressivenessYes 1 1.1781e+14 9.6677e+15 13631
## - I(APG^2) 1 1.3481e+14 9.6847e+15 13631
## - PPG:BPG 1 1.6259e+14 9.7125e+15 13633
## - MPG:APG 1 1.7019e+14 9.7201e+15 13633
## - PPG:AgressivenessYes 1 1.8644e+14 9.7363e+15 13634
## - PPG:SPG 1 2.0727e+14 9.7571e+15 13635
## - PPG:TOPG 1 2.9668e+14 9.8466e+15 13639## Warning: In lm.fit(x, y, offset = offset, singular.ok = singular.ok, ...) :
## extra argument 'trControl' will be disregarded##
## Step: AIC=13625.56
## Salary17_18 ~ MPG + PPG + APG + RPG + TOPG + BPG + SPG + TrustedYes +
## AgressivenessYes + I(APG^2) + MPG:APG + MPG:BPG + MPG:SPG +
## MPG:TrustedYes + MPG:AgressivenessYes + PPG:TOPG + PPG:BPG +
## PPG:SPG + PPG:AgressivenessYes + APG:SPG + APG:AgressivenessYes +
## RPG:SPG + TOPG:BPG + BPG:SPG + BPG:TrustedYes + BPG:AgressivenessYes
##
## Df Sum of Sq RSS AIC
## - BPG:SPG 1 3.0129e+13 9.5884e+15 13625
## - RPG:SPG 1 4.2226e+13 9.6005e+15 13626
## - MPG:BPG 1 4.3179e+13 9.6015e+15 13626
## <none> 9.5583e+15 13626
## - MPG:TrustedYes 1 4.5682e+13 9.6040e+15 13626
## - BPG:TrustedYes 1 5.6003e+13 9.6143e+15 13626
## + APG:TOPG 1 1.9637e+13 9.5387e+15 13627
## - MPG:AgressivenessYes 1 7.1085e+13 9.6294e+15 13627
## + RPG:TrustedYes 1 1.2994e+13 9.5453e+15 13627
## + APG:BPG 1 1.0543e+13 9.5478e+15 13627
## + APG:TrustedYes 1 1.0346e+13 9.5480e+15 13627
## + RPG:AgressivenessYes 1 8.7250e+12 9.5496e+15 13627
## + I(BPG^2) 1 8.4322e+12 9.5499e+15 13627
## + SPG:TrustedYes 1 8.1565e+12 9.5502e+15 13627
## + TOPG:SPG 1 7.5648e+12 9.5507e+15 13627
## + I(RPG^2) 1 7.5008e+12 9.5508e+15 13627
## + I(TOPG^2) 1 5.8335e+12 9.5525e+15 13627
## + RPG:BPG 1 5.7185e+12 9.5526e+15 13627
## + SPG:AgressivenessYes 1 4.5618e+12 9.5538e+15 13627
## + TOPG:TrustedYes 1 4.0192e+12 9.5543e+15 13627
## - MPG:SPG 1 8.3329e+13 9.6416e+15 13627
## + I(SPG^2) 1 3.1280e+12 9.5552e+15 13627
## + PPG:RPG 1 1.0280e+12 9.5573e+15 13628
## + PPG:APG 1 1.0072e+12 9.5573e+15 13628
## + TrustedYes:AgressivenessYes 1 9.6238e+11 9.5574e+15 13628
## + MPG:TOPG 1 6.7199e+11 9.5576e+15 13628
## + APG:RPG 1 6.1019e+11 9.5577e+15 13628
## + MPG:RPG 1 5.6357e+11 9.5578e+15 13628
## + TOPG:AgressivenessYes 1 1.5113e+11 9.5582e+15 13628
## + RPG:TOPG 1 1.0857e+11 9.5582e+15 13628
## + I(MPG^2) 1 7.4969e+10 9.5582e+15 13628
## + I(PPG^2) 1 2.0627e+10 9.5583e+15 13628
## + PPG:TrustedYes 1 3.6299e+09 9.5583e+15 13628
## + MPG:PPG 1 8.7576e+07 9.5583e+15 13628
## - BPG:AgressivenessYes 1 8.8791e+13 9.6471e+15 13628
## - TOPG:BPG 1 9.1166e+13 9.6495e+15 13628
## - APG:SPG 1 1.0279e+14 9.6611e+15 13628
## - APG:AgressivenessYes 1 1.2308e+14 9.6814e+15 13629
## - I(APG^2) 1 1.2731e+14 9.6856e+15 13629
## - PPG:BPG 1 1.5769e+14 9.7160e+15 13631
## - PPG:AgressivenessYes 1 1.8260e+14 9.7409e+15 13632
## - MPG:APG 1 2.0028e+14 9.7586e+15 13633
## - PPG:SPG 1 2.0990e+14 9.7682e+15 13633
## - PPG:TOPG 1 2.9213e+14 9.8504e+15 13637## Warning: In lm.fit(x, y, offset = offset, singular.ok = singular.ok, ...) :
## extra argument 'trControl' will be disregarded##
## Step: AIC=13624.95
## Salary17_18 ~ MPG + PPG + APG + RPG + TOPG + BPG + SPG + TrustedYes +
## AgressivenessYes + I(APG^2) + MPG:APG + MPG:BPG + MPG:SPG +
## MPG:TrustedYes + MPG:AgressivenessYes + PPG:TOPG + PPG:BPG +
## PPG:SPG + PPG:AgressivenessYes + APG:SPG + APG:AgressivenessYes +
## RPG:SPG + TOPG:BPG + BPG:TrustedYes + BPG:AgressivenessYes
##
## Df Sum of Sq RSS AIC
## - RPG:SPG 1 1.8257e+13 9.6067e+15 13624
## - MPG:BPG 1 2.1829e+13 9.6103e+15 13624
## <none> 9.5884e+15 13625
## + BPG:SPG 1 3.0129e+13 9.5583e+15 13626
## - TOPG:BPG 1 6.6228e+13 9.6547e+15 13626
## - MPG:TrustedYes 1 6.7101e+13 9.6555e+15 13626
## - MPG:AgressivenessYes 1 6.7695e+13 9.6561e+15 13626
## + I(RPG^2) 1 1.7106e+13 9.5713e+15 13626
## - BPG:TrustedYes 1 7.0657e+13 9.6591e+15 13626
## + RPG:BPG 1 1.5265e+13 9.5732e+15 13626
## + SPG:TrustedYes 1 1.0670e+13 9.5778e+15 13626
## + APG:TrustedYes 1 9.2209e+12 9.5792e+15 13626
## + APG:TOPG 1 9.2196e+12 9.5792e+15 13626
## - BPG:AgressivenessYes 1 7.8460e+13 9.6669e+15 13626
## - MPG:SPG 1 8.1554e+13 9.6700e+15 13627
## + PPG:RPG 1 4.9724e+12 9.5835e+15 13627
## + RPG:TrustedYes 1 4.9460e+12 9.5835e+15 13627
## + SPG:AgressivenessYes 1 4.5314e+12 9.5839e+15 13627
## + RPG:AgressivenessYes 1 4.1073e+12 9.5843e+15 13627
## + TOPG:TrustedYes 1 3.6638e+12 9.5848e+15 13627
## + I(TOPG^2) 1 3.5690e+12 9.5849e+15 13627
## + TOPG:SPG 1 3.5298e+12 9.5849e+15 13627
## + I(SPG^2) 1 2.2058e+12 9.5862e+15 13627
## + MPG:RPG 1 1.9908e+12 9.5865e+15 13627
## + RPG:TOPG 1 1.5761e+12 9.5869e+15 13627
## + PPG:APG 1 1.3125e+12 9.5871e+15 13627
## + I(BPG^2) 1 1.1909e+12 9.5873e+15 13627
## + TrustedYes:AgressivenessYes 1 7.7205e+11 9.5877e+15 13627
## + MPG:TOPG 1 6.4047e+11 9.5878e+15 13627
## + APG:RPG 1 5.3888e+11 9.5879e+15 13627
## + APG:BPG 1 1.8631e+11 9.5883e+15 13627
## + I(MPG^2) 1 1.6169e+11 9.5883e+15 13627
## + TOPG:AgressivenessYes 1 6.6052e+10 9.5884e+15 13627
## + I(PPG^2) 1 2.5138e+10 9.5884e+15 13627
## + MPG:PPG 1 2.2387e+10 9.5884e+15 13627
## + PPG:TrustedYes 1 1.3072e+09 9.5884e+15 13627
## - APG:SPG 1 8.8058e+13 9.6765e+15 13627
## - APG:AgressivenessYes 1 1.2271e+14 9.7112e+15 13629
## - I(APG^2) 1 1.2901e+14 9.7174e+15 13629
## - PPG:BPG 1 1.3774e+14 9.7262e+15 13629
## - PPG:AgressivenessYes 1 1.7464e+14 9.7631e+15 13631
## - MPG:APG 1 1.7651e+14 9.7649e+15 13631
## - PPG:SPG 1 1.9761e+14 9.7861e+15 13632
## - PPG:TOPG 1 2.6335e+14 9.8518e+15 13635## Warning: In lm.fit(x, y, offset = offset, singular.ok = singular.ok, ...) :
## extra argument 'trControl' will be disregarded##
## Step: AIC=13623.79
## Salary17_18 ~ MPG + PPG + APG + RPG + TOPG + BPG + SPG + TrustedYes +
## AgressivenessYes + I(APG^2) + MPG:APG + MPG:BPG + MPG:SPG +
## MPG:TrustedYes + MPG:AgressivenessYes + PPG:TOPG + PPG:BPG +
## PPG:SPG + PPG:AgressivenessYes + APG:SPG + APG:AgressivenessYes +
## TOPG:BPG + BPG:TrustedYes + BPG:AgressivenessYes
##
## Df Sum of Sq RSS AIC
## - MPG:BPG 1 3.0269e+13 9.6370e+15 13623
## <none> 9.6067e+15 13624
## - MPG:TrustedYes 1 5.8085e+13 9.6648e+15 13624
## + I(RPG^2) 1 2.5182e+13 9.5815e+15 13625
## - BPG:TrustedYes 1 6.2902e+13 9.6696e+15 13625
## - MPG:SPG 1 6.3352e+13 9.6701e+15 13625
## - MPG:AgressivenessYes 1 6.3611e+13 9.6703e+15 13625
## + RPG:SPG 1 1.8257e+13 9.5884e+15 13625
## + PPG:RPG 1 1.4100e+13 9.5926e+15 13625
## + RPG:BPG 1 1.3506e+13 9.5932e+15 13625
## + SPG:TrustedYes 1 1.2489e+13 9.5942e+15 13625
## - BPG:AgressivenessYes 1 7.5236e+13 9.6819e+15 13625
## - TOPG:BPG 1 7.6211e+13 9.6829e+15 13625
## + APG:TOPG 1 1.0818e+13 9.5959e+15 13625
## + RPG:TOPG 1 1.0693e+13 9.5960e+15 13625
## + APG:TrustedYes 1 9.4749e+12 9.5972e+15 13625
## + MPG:RPG 1 8.6781e+12 9.5980e+15 13625
## + TOPG:SPG 1 7.0638e+12 9.5996e+15 13626
## + BPG:SPG 1 6.1590e+12 9.6005e+15 13626
## + TOPG:TrustedYes 1 4.1811e+12 9.6025e+15 13626
## + I(SPG^2) 1 4.1345e+12 9.6026e+15 13626
## + I(TOPG^2) 1 3.8757e+12 9.6028e+15 13626
## + I(BPG^2) 1 3.0415e+12 9.6037e+15 13626
## + APG:BPG 1 2.4489e+12 9.6043e+15 13626
## + APG:RPG 1 2.0024e+12 9.6047e+15 13626
## + SPG:AgressivenessYes 1 1.6004e+12 9.6051e+15 13626
## + MPG:TOPG 1 1.2868e+12 9.6054e+15 13626
## + PPG:APG 1 1.0059e+12 9.6057e+15 13626
## + TrustedYes:AgressivenessYes 1 6.0185e+11 9.6061e+15 13626
## + RPG:TrustedYes 1 2.3715e+11 9.6065e+15 13626
## + RPG:AgressivenessYes 1 1.3855e+11 9.6066e+15 13626
## + TOPG:AgressivenessYes 1 8.6826e+10 9.6066e+15 13626
## + I(MPG^2) 1 2.0696e+10 9.6067e+15 13626
## + PPG:TrustedYes 1 1.1809e+10 9.6067e+15 13626
## + I(PPG^2) 1 9.8169e+09 9.6067e+15 13626
## + MPG:PPG 1 5.5853e+08 9.6067e+15 13626
## - APG:SPG 1 1.1595e+14 9.7227e+15 13627
## - APG:AgressivenessYes 1 1.1902e+14 9.7257e+15 13627
## - PPG:BPG 1 1.4072e+14 9.7474e+15 13628
## - I(APG^2) 1 1.4223e+14 9.7489e+15 13628
## - MPG:APG 1 1.6421e+14 9.7709e+15 13629
## - PPG:AgressivenessYes 1 1.6734e+14 9.7740e+15 13629
## - PPG:SPG 1 2.0086e+14 9.8076e+15 13631
## - PPG:TOPG 1 2.4642e+14 9.8531e+15 13633
## - RPG 1 4.7769e+14 1.0084e+16 13643## Warning: In lm.fit(x, y, offset = offset, singular.ok = singular.ok, ...) :
## extra argument 'trControl' will be disregarded##
## Step: AIC=13623.18
## Salary17_18 ~ MPG + PPG + APG + RPG + TOPG + BPG + SPG + TrustedYes +
## AgressivenessYes + I(APG^2) + MPG:APG + MPG:SPG + MPG:TrustedYes +
## MPG:AgressivenessYes + PPG:TOPG + PPG:BPG + PPG:SPG + PPG:AgressivenessYes +
## APG:SPG + APG:AgressivenessYes + TOPG:BPG + BPG:TrustedYes +
## BPG:AgressivenessYes
##
## Df Sum of Sq RSS AIC
## <none> 9.6370e+15 13623
## + I(RPG^2) 1 4.0755e+13 9.5962e+15 13623
## + RPG:BPG 1 3.2462e+13 9.6045e+15 13624
## - TOPG:BPG 1 5.5278e+13 9.6922e+15 13624
## - MPG:AgressivenessYes 1 5.6598e+13 9.6936e+15 13624
## + MPG:BPG 1 3.0269e+13 9.6067e+15 13624
## - MPG:SPG 1 5.8008e+13 9.6950e+15 13624
## - BPG:AgressivenessYes 1 5.9268e+13 9.6962e+15 13624
## + RPG:SPG 1 2.6697e+13 9.6103e+15 13624
## + MPG:RPG 1 2.6005e+13 9.6110e+15 13624
## + PPG:RPG 1 1.8795e+13 9.6182e+15 13624
## + RPG:TOPG 1 1.5239e+13 9.6217e+15 13624
## + APG:TOPG 1 1.4769e+13 9.6222e+15 13624
## - MPG:TrustedYes 1 7.3838e+13 9.7108e+15 13625
## + APG:TrustedYes 1 9.2494e+12 9.6277e+15 13625
## + TOPG:SPG 1 9.0400e+12 9.6279e+15 13625
## + TOPG:TrustedYes 1 7.5608e+12 9.6294e+15 13625
## + APG:BPG 1 6.4859e+12 9.6305e+15 13625
## + SPG:TrustedYes 1 4.9391e+12 9.6320e+15 13625
## + I(SPG^2) 1 4.8687e+12 9.6321e+15 13625
## + PPG:APG 1 3.3978e+12 9.6336e+15 13625
## + SPG:AgressivenessYes 1 3.0211e+12 9.6339e+15 13625
## + APG:RPG 1 2.6198e+12 9.6343e+15 13625
## + I(MPG^2) 1 1.8825e+12 9.6351e+15 13625
## + I(TOPG^2) 1 1.3308e+12 9.6356e+15 13625
## + MPG:PPG 1 3.8245e+11 9.6366e+15 13625
## + RPG:TrustedYes 1 3.5643e+11 9.6366e+15 13625
## + MPG:TOPG 1 1.8714e+11 9.6368e+15 13625
## + I(PPG^2) 1 6.7831e+10 9.6369e+15 13625
## + BPG:SPG 1 6.4782e+10 9.6369e+15 13625
## + RPG:AgressivenessYes 1 5.7643e+10 9.6369e+15 13625
## + PPG:TrustedYes 1 5.3417e+10 9.6369e+15 13625
## + TOPG:AgressivenessYes 1 3.4254e+10 9.6369e+15 13625
## + TrustedYes:AgressivenessYes 1 1.9170e+09 9.6370e+15 13625
## + I(BPG^2) 1 1.3607e+09 9.6370e+15 13625
## - PPG:BPG 1 1.1230e+14 9.7493e+15 13626
## - APG:AgressivenessYes 1 1.1261e+14 9.7496e+15 13626
## - APG:SPG 1 1.1865e+14 9.7556e+15 13627
## - I(APG^2) 1 1.4611e+14 9.7831e+15 13628
## - MPG:APG 1 1.5359e+14 9.7906e+15 13628
## - PPG:AgressivenessYes 1 1.5778e+14 9.7948e+15 13628
## - BPG:TrustedYes 1 1.9502e+14 9.8320e+15 13630
## - PPG:SPG 1 1.9892e+14 9.8359e+15 13630
## - PPG:TOPG 1 2.3613e+14 9.8731e+15 13632
## - RPG 1 4.8769e+14 1.0125e+16 13643summary(model_stepwise)##
## Call:
## lm(formula = Salary17_18 ~ MPG + PPG + APG + RPG + TOPG + BPG +
## SPG + TrustedYes + AgressivenessYes + I(APG^2) + MPG:APG +
## MPG:SPG + MPG:TrustedYes + MPG:AgressivenessYes + PPG:TOPG +
## PPG:BPG + PPG:SPG + PPG:AgressivenessYes + APG:SPG + APG:AgressivenessYes +
## TOPG:BPG + BPG:TrustedYes + BPG:AgressivenessYes, data = per_game_stats,
## trControl = train_control)
##
## Residuals:
## Min 1Q Median 3Q Max
## -14937985 -2273358 -461127 2318966 18582921
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -543468 1186172 -0.458 0.64707
## MPG 180653 133652 1.352 0.17721
## PPG -59682 251745 -0.237 0.81272
## APG -1969636 1092244 -1.803 0.07206 .
## RPG 818296 177918 4.599 5.63e-06 ***
## TOPG -391774 1612970 -0.243 0.80821
## BPG -73317 1612103 -0.045 0.96375
## SPG 2663406 3261544 0.817 0.41462
## TrustedYes -11599960 4748465 -2.443 0.01498 *
## AgressivenessYes 5902362 3551177 1.662 0.09725 .
## I(APG^2) 283784 112728 2.517 0.01219 *
## MPG:APG 137917 53434 2.581 0.01019 *
## MPG:SPG -281745 177621 -1.586 0.11345
## MPG:TrustedYes 392843 219513 1.790 0.07424 .
## MPG:AgressivenessYes -296519 189250 -1.567 0.11791
## PPG:TOPG -274828 85875 -3.200 0.00148 **
## PPG:BPG -363323 164619 -2.207 0.02785 *
## PPG:SPG 672283 228872 2.937 0.00349 **
## PPG:AgressivenessYes 733673 280450 2.616 0.00922 **
## APG:SPG -1325717 584378 -2.269 0.02380 *
## APG:AgressivenessYes -1885903 853314 -2.210 0.02764 *
## TOPG:BPG 1979001 1278068 1.548 0.12228
## BPG:TrustedYes 6520298 2241878 2.908 0.00383 **
## BPG:AgressivenessYes -3907032 2436786 -1.603 0.10961
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 4802000 on 418 degrees of freedom
## Multiple R-squared: 0.6192, Adjusted R-squared: 0.5983
## F-statistic: 29.56 on 23 and 418 DF, p-value: < 2.2e-16Best model
stepwise_model <- lm(formula = Salary17_18 ~ MPG + PPG + APG + RPG + TOPG + BPG +
SPG + TrustedYes + AgressivenessYes + I(APG^2) + MPG:APG +
MPG:SPG + MPG:TrustedYes + MPG:AgressivenessYes + PPG:TOPG +
PPG:BPG + PPG:SPG + PPG:AgressivenessYes + APG:SPG + APG:AgressivenessYes +
TOPG:BPG + BPG:TrustedYes + BPG:AgressivenessYes, data = per_game_stats,
trControl = train_control)## Warning: In lm.fit(x, y, offset = offset, singular.ok = singular.ok, ...) :
## extra argument 'trControl' will be disregardedsummary(stepwise_model)##
## Call:
## lm(formula = Salary17_18 ~ MPG + PPG + APG + RPG + TOPG + BPG +
## SPG + TrustedYes + AgressivenessYes + I(APG^2) + MPG:APG +
## MPG:SPG + MPG:TrustedYes + MPG:AgressivenessYes + PPG:TOPG +
## PPG:BPG + PPG:SPG + PPG:AgressivenessYes + APG:SPG + APG:AgressivenessYes +
## TOPG:BPG + BPG:TrustedYes + BPG:AgressivenessYes, data = per_game_stats,
## trControl = train_control)
##
## Residuals:
## Min 1Q Median 3Q Max
## -14937985 -2273358 -461127 2318966 18582921
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -543468 1186172 -0.458 0.64707
## MPG 180653 133652 1.352 0.17721
## PPG -59682 251745 -0.237 0.81272
## APG -1969636 1092244 -1.803 0.07206 .
## RPG 818296 177918 4.599 5.63e-06 ***
## TOPG -391774 1612970 -0.243 0.80821
## BPG -73317 1612103 -0.045 0.96375
## SPG 2663406 3261544 0.817 0.41462
## TrustedYes -11599960 4748465 -2.443 0.01498 *
## AgressivenessYes 5902362 3551177 1.662 0.09725 .
## I(APG^2) 283784 112728 2.517 0.01219 *
## MPG:APG 137917 53434 2.581 0.01019 *
## MPG:SPG -281745 177621 -1.586 0.11345
## MPG:TrustedYes 392843 219513 1.790 0.07424 .
## MPG:AgressivenessYes -296519 189250 -1.567 0.11791
## PPG:TOPG -274828 85875 -3.200 0.00148 **
## PPG:BPG -363323 164619 -2.207 0.02785 *
## PPG:SPG 672283 228872 2.937 0.00349 **
## PPG:AgressivenessYes 733673 280450 2.616 0.00922 **
## APG:SPG -1325717 584378 -2.269 0.02380 *
## APG:AgressivenessYes -1885903 853314 -2.210 0.02764 *
## TOPG:BPG 1979001 1278068 1.548 0.12228
## BPG:TrustedYes 6520298 2241878 2.908 0.00383 **
## BPG:AgressivenessYes -3907032 2436786 -1.603 0.10961
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 4802000 on 418 degrees of freedom
## Multiple R-squared: 0.6192, Adjusted R-squared: 0.5983
## F-statistic: 29.56 on 23 and 418 DF, p-value: < 2.2e-16Model Performance: The model’s r-squared value is 0.6192, and the adjusted r-squared is 0.5983. This means that the predictors in the model explain about 61.92% of the variation in player salaries, showing that it captures a substantial portion of the influencing factors.
Key Predictors: Certain variables, like rebounds per game (RPG), show a strong positive relationship with salary. This indicates that players who excel at rebounding tend to earn more.
Interaction Effects: The model includes interaction terms such as PPG (points per game and steals per game) and PPG (points per game and aggressive play style). These significant interactions demonstrate that specific skill combinations can increase player salaries.
Second-Order Terms: The model includes second-order terms like I(APG2)I(APG^2)I(APG2) (assists per game squared). These terms help capture non-linear relationships, where the effect of assists on salary changes at higher levels.
Model Robustness: The strong F-statistic (p-value < 2.2e-16) confirms that the model, as a whole, is statistically significant and the predictors contribute meaningful information for salary prediction.
RandomForest
library(dplyr)
rf_data <- per_game_stats %>% select( MPG, PPG, APG, RPG, TOPG, BPG, SPG, TrustedYes, AgressivenessYes, Salary17_18)
head(rf_data)## MPG PPG APG RPG TOPG BPG SPG
## 1 7.409091 2.181818 0.1818182 1.636364 0.4545455 0.5909091 0.04545455
## 2 13.753846 4.953846 1.9230769 1.061538 1.0153846 0.1384615 0.38461538
## 3 28.725000 12.737500 1.8750000 5.062500 1.1125000 0.5000000 0.80000000
## 4 29.065574 8.721311 1.6229508 7.393443 1.5409836 0.7213115 0.98360656
## 5 32.250000 14.000000 4.9558824 6.823529 1.7058824 1.2794118 0.76470588
## 6 14.106061 8.106061 0.8636364 4.212121 0.5000000 0.2424242 0.28787879
## TrustedYes AgressivenessYes Salary17_18
## 1 0 0 1312611
## 2 0 0 2116955
## 3 1 0 5504420
## 4 1 1 7319035
## 5 1 1 27734405
## 6 0 0 9769821library(randomForest)## randomForest 4.7-1.2## Type rfNews() to see new features/changes/bug fixes.##
## Attaching package: 'randomForest'## The following object is masked from 'package:ggplot2':
##
## margin## The following object is masked from 'package:dplyr':
##
## combinerf_model <- randomForest(Salary17_18 ~ ., data = rf_data, ntree = 500)
print(rf_model)##
## Call:
## randomForest(formula = Salary17_18 ~ ., data = rf_data, ntree = 500)
## Type of random forest: regression
## Number of trees: 500
## No. of variables tried at each split: 3
##
## Mean of squared residuals: 2.66485e+13
## % Var explained: 53.46predictions <- predict(rf_model, rf_data)
rmse <- sqrt(mean((predictions - rf_data$Salary17_18)^2))
cat("RMSE: ", rmse, "\n")## RMSE: 2350629rsq <- 1 - sum((predictions - rf_data$Salary17_18)^2) / sum((rf_data$Salary17_18 - mean(rf_data$Salary17_18))^2)
cat("R-squared: ", rsq, "\n")## R-squared: 0.9035066Mean of Squared Residuals: The mean squared residual (error) is 2.637338e+13 which gives an idea of how well the model is fitting the data (lower values are better).
The model explains 53.94% of the variance in the target variable (Salary17_18). This indicates that the model captures just over half of the variability in the target variable, which is useful but not perfect.
RMSE (Root Mean Squared Error): The RMSE is 2,334,881, which measures the average magnitude of the error between the predicted and actual values. This indicates how far off, on average, the predictions are from the actual values.
R-squared: The R² value of 0.9048 is very high, indicating that about 90.48% of the variance in salary can be explained by the model’s features.
Accuracy comparison
let’s create a predicted columns for both the models
predict_salary_rf <- function(point, minutes, turn_over, rebounds, assists, block, steal, TrustedYes, AgressivenessYes) {
predict(rf_model, data.frame(PPG = point, MPG = minutes, TOPG = turn_over, RPG = rebounds, SPG = steal,
APG = assists, BPG = block, TrustedYes = TrustedYes, AgressivenessYes = AgressivenessYes))
}
per_game_stats$rf_Predicted_Salary <- mapply(predict_salary_rf,
point = per_game_stats$PPG,
minutes = per_game_stats$MPG,
turn_over = per_game_stats$TOPG,
rebounds = per_game_stats$RPG,
assists = per_game_stats$APG,
block = per_game_stats$BPG,
steal = per_game_stats$SPG,
TrustedYes = per_game_stats$TrustedYes,
AgressivenessYes = per_game_stats$AgressivenessYes)
predict_salary_stepwise <- function(point, minutes, turn_over, rebounds, assists, block, steal, TrustedYes, AgressivenessYes) {
predict(stepwise_model, data.frame(PPG = point, MPG = minutes, TOPG = turn_over, RPG = rebounds, SPG = steal,
APG = assists, BPG = block, TrustedYes = TrustedYes, AgressivenessYes = AgressivenessYes))
}
per_game_stats$stepwise_Predicted_Salary <- mapply(predict_salary_stepwise,
point = per_game_stats$PPG,
minutes = per_game_stats$MPG,
turn_over = per_game_stats$TOPG,
rebounds = per_game_stats$RPG,
assists = per_game_stats$APG,
block = per_game_stats$BPG,
steal = per_game_stats$SPG,
TrustedYes = per_game_stats$TrustedYes,
AgressivenessYes = per_game_stats$AgressivenessYes)
head(per_game_stats)## Player Team MPG PPG APG RPG TOPG
## 1 A.J. Hammons DAL 7.409091 2.181818 0.1818182 1.636364 0.4545455
## 2 Aaron Brooks IND 13.753846 4.953846 1.9230769 1.061538 1.0153846
## 3 Aaron Gordon ORL 28.725000 12.737500 1.8750000 5.062500 1.1125000
## 4 Al-Farouq Aminu POR 29.065574 8.721311 1.6229508 7.393443 1.5409836
## 5 Al Horford BOS 32.250000 14.000000 4.9558824 6.823529 1.7058824
## 6 Al Jefferson IND 14.106061 8.106061 0.8636364 4.212121 0.5000000
## BPG SPG TrustedYes AgressivenessYes Salary17_18 Cluster
## 1 0.5909091 0.04545455 0 0 1312611 2
## 2 0.1384615 0.38461538 0 0 2116955 2
## 3 0.5000000 0.80000000 1 0 5504420 2
## 4 0.7213115 0.98360656 1 1 7319035 2
## 5 1.2794118 0.76470588 1 1 27734405 3
## 6 0.2424242 0.28787879 0 0 9769821 1
## rf_Predicted_Salary stepwise_Predicted_Salary
## 1 1482978 1491947
## 2 1865646 1496801
## 3 6844990 10643725
## 4 9303577 10398142
## 5 20956951 18707029
## 6 6776402 4218798library(ggplot2)
library(gridExtra)##
## Attaching package: 'gridExtra'## The following object is masked from 'package:randomForest':
##
## combine## The following object is masked from 'package:dplyr':
##
## combineplot_rf <- ggplot(per_game_stats) +
geom_point(aes(x = Salary17_18, y = rf_Predicted_Salary), color = "blue", alpha = 0.6) +
geom_abline(slope = 1, intercept = 0, color = "red", linetype = "dashed") +
labs(title = "Random Forest: Actual vs Predicted Salaries", x = "Actual Salary", y = "Predicted Salary (RF)") +
theme_minimal() + theme(plot.title = element_text(hjust = 0.5))
plot_stepwise <- ggplot(per_game_stats) +
geom_point(aes(x = Salary17_18, y = stepwise_Predicted_Salary), color = "green", alpha = 0.6) +
geom_abline(slope = 1, intercept = 0, color = "red", linetype = "dashed") +
labs(title = "Stepwise: Actual vs Predicted Salaries", x = "Actual Salary", y = "Predicted Salary (Stepwise)") +
theme_minimal() + theme(plot.title = element_text(hjust = 0.5))
grid.arrange(plot_rf, plot_stepwise, ncol = 2)
Random Forest:
The predicted values closely align with the actual values, especially for low-to-mid-range salaries, suggesting high accuracy. Slight deviations occur at the higher salary range.
Stepwise Regression:
The predictions are more dispersed around the red line, indicating lower accuracy and higher variance. It struggles with higher salaries, showing significant underprediction.
Overall, the Random Forest model outperforms Stepwise Regression in terms of predictive accuracy and consistency.
g. Evaluation
summary(rf_data$Salary17_18)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 17224 1518316 3519283 7106258 10812701 34682550Let’s set the median as the threshold for our classification of salaries.
threshold <- 3519283
rf_data$Salary_Class <- ifelse(rf_data$Salary17_18 > threshold, "High Salary", "Low Salary")
rf_data$Salary_Class <- factor(rf_data$Salary_Class)
predictions <- predict(rf_model, rf_data)
predicted_class <- ifelse(predictions > threshold, "High Salary", "Low Salary")
predicted_class <- factor(predicted_class, levels = c("Low Salary", "High Salary"))A salary class column is created based on weather the salary is above or below the threshold.
The rf_model is used to make the predictions.
Predictions are also classified as high or low based on the same threshold.
conf_matrix <- table(Predicted = predicted_class, Actual = rf_data$Salary_Class)
print(conf_matrix)## Actual
## Predicted High Salary Low Salary
## Low Salary 2 171
## High Salary 219 50The confusion matrix indicates that the model has a relatively high number of false positives (219) for “High Salary” and true negatives (167) for “Low Salary.” The recall is quite high (0.99), meaning it successfully identifies most players with “High Salary,” but the precision (0.80) suggests that it misclassifies some players as “High Salary” when they actually belong in the “Low Salary” category.
TP <- conf_matrix["High Salary", "High Salary"]
TN <- conf_matrix["Low Salary", "Low Salary"]
FP <- conf_matrix["High Salary", "Low Salary"]
FN <- conf_matrix["Low Salary", "High Salary"]
precision <- TP / (TP + FP)
recall <- TP / (TP + FN)
cat("Precision: ", precision, "\n")## Precision: 0.8141264cat("Recall: ", recall, "\n")## Recall: 0.9909502Precision (0.80): This means that 80% of the players predicted as “High Salary” actually have a high salary. It’s a measure of the model’s accuracy in identifying “High Salary” players without making too many mistakes (false positives).
Recall (0.99): This indicates that the model correctly identified 99% of the actual “High Salary” players. It’s a measure of the model’s ability to capture most of the true “High Salary” players, even if it makes some false positives.
The model has a very high recall, meaning it successfully identifies most high-salary players. However, with a precision of 80%, it occasionally misclassifies lower salary players as high salary. While the model excels at recognizing high salary players, improving its precision by reducing false positives would lead to better performance overall.
library(pROC)## Type 'citation("pROC")' for a citation.##
## Attaching package: 'pROC'## The following objects are masked from 'package:stats':
##
## cov, smooth, varprobabilities <- predict(rf_model, rf_data, type = "response")
roc_curve <- roc(rf_data$Salary_Class, probabilities)## Setting levels: control = High Salary, case = Low Salary## Setting direction: controls > casesplot(roc_curve, main = "ROC Curve")
Curve Shape: The curve is close to the top-left corner, indicating strong model performance. Diagonal Reference Line: The diagonal represents random guessing. Your curve being above this line shows the model performs better than random.
Area Under Curve (AUC): Though not explicitly mentioned, the shape suggests a high AUC, reflecting good discrimination between high and low salary classes.
The model has excellent sensitivity and precision (as seen in prior metrics), and the ROC curve confirms its ability to distinguish between salary classes effectively. However, the imbalance in misclassification rates (notably, high false positives for “High Salary”) should be considered for refinement.
Report
1.Introduction
This project involves building a predictive model to estimate NBA player salaries for the 2017- 2018 season. The prediction is based on player performance data from the 2016-2017 season, allowing us to assess how past performance influences future earnings.
Objective:
To develop a model that can predict the 2017-2018 season salaries of NBA players using their statistics from the previous season. Understanding the relationship between player performance and salary can provide insights into the factors that NBA teams consider when compensating players. It highlights which performance metrics are most valued and how they contribute to a player’s market worth, guiding both management decisions and player career strategies.
2.Data Gathering and Integration
Two primary datasets were used:
a.Stats dataset: Contains detailed performance metrics for NBA players from 1950 to 2017.
b.Salary_1718 dataset: Includes salaries of NBA players for the 2017-2018 season. The datasets were filtered to focus on the 2016-2017 season stats and merged based on player names.
3.Data Cleaning and Preprocessing
1.Removal of unnecessary columns (e.g., Team).
2.Handling of 32 NA values by replacing them with column means.
3.Creation of per-game statistics (e.g., PPG, MPG, APG) to normalize player performance.
4.Introduction of derived variables: “Aggressiveness”: Based on above-average turnovers per game. “Trusted”: Based on above-average minutes per game.
4.Data Exploration
Correlation analysis revealed:
Strongest correlations with salary: PPG > MPG > TOPG > RPG > PER > SPG > APG
Positive correlation between turnovers and salary, interpreted as a sign of player involvement Visualization of PPG vs. salary showed a general upward trend, indicating higher salaries for players with higher scoring averages.
5.Clustering Analysis
The optimal number of clusters was determined using two methods:
Elbow Method: Suggested 3 clusters as optimal.
Silhouette Method: Confirmed 3 clusters as optimal.
Clustering observations revealed:
Cluster 1 (Red): Compact group, mostly trusted players
Cluster 2 (Green): Spread-out group, mix of trusted and non-trusted players
Cluster 3 (Blue): Separated group, almost entirely trusted and aggressive players
6.Classification Models
Two classification models were developed:
Stepwise Regression Model:
R-squared: 0.6192
Adjusted R-squared: 0.5983
Key predictors: RPG, PPG interactions, APG squared
Random Forest Model:
Mean Squared Residuals: 2.637338e+13
Variance explained: 53.94%
R-squared: 0.9048
The Random Forest model outperformed the Stepwise Regression model in terms of predictive accuracy and consistency.
7.Model Evaluation
A threshold of $351,983 (median salary) was set to classify salaries as high or low. The Random Forest model was evaluated using various metrics:
Precision: 0.80
Recall: 0.99
ROC curve: Showed strong model performance with a curve close to the top-left corner The model excelled at identifying high-salary players but occasionally misclassified lower salary players as high salary.
.8.Conclusion
This project demonstrated the effectiveness of machine learning techniques in predicting NBA player salaries based on performance metrics. The Random Forest model showed superior performance, explaining about 90% of the variance in salaries. The analysis highlighted the importance of scoring, rebounding, and playing time in determining a player’s market value. Future refinements could focus on reducing false positives in high salary predictions to improve overall model accuracy.
i. Reflection
This Project emphasized the importance of data preparation, from cleaning to visualization, and taught the nuances of unsupervised and supervised techniques. Through hands-on work, I strengthened my R programming skills and gained deeper insights into clustering and classification. The journey underscored the value of metrices like precision and Roc in complementing accuracy for model evaluation.
Fundamental of Data Science as a course has provided a solid foundation for data science principles and practices. The hands-on experience with working with real world data as assignments and projects has been invaluable, bridging the gap between theory and applications. As I move forward in my data science journey, I am confident that these skills and experiences will serve as a strong basis of tackling more complex challenges and contributing meaningfully to my future projects.